Fresnel lens, screen, image display device, lens mold manufacturing method and lens manufacturing method

ABSTRACT

A Fresnel lens has a plurality of pitch areas in which a plurality of hybrid type prism portions are arranged. Each hybrid type prism portion has a refraction type prism portion and a total reflection type prism portion. In the refraction type prism portion, a ray of incident light Li 1  of an incident angle “an” is refracted twice and goes out as a ray of outgoing light Lo 1  of an outgoing angle “f”. In the total reflection type prism portion, a ray of incident light Li 2  of the incident angle “a” is refracted, totally reflected and refracted in that order and goes out as a ray of outgoing light Lo 2  parallel to the ray of outgoing light Lo 1.

This application is the national phase under 35 U.S.C. § 371 of PCTInternational Application No. PCT/JP01/08578 which has an Internationalfiling date of Sep. 28, 2001, which designated the United States ofAmerica.

TECHNICAL FIELD

The present invention relates to a Fresnel lens having the same functionas a convex lens almost without requiring a distance between alightincident point and alight out going point. Also, the present inventionrelates to a rear projection type screen, to which the Fresnel lens isapplied, and an image displaying device to which the screen is applied.In addition, the present invention relates to a lens forming moldmanufacturing method and a lens manufacturing method.

BACKGROUND ART

In an image displaying device represented by a rear projection typeprojection television, a screen is used, and image light emitted from animage light source is projected on the screen. In general, the screen ofthe image displaying device is formed by combining a lenticular and aFresnel lens. The lenticular functions as a light diffusion plate inwhich the image light is scattered to form an image. In the Fresnellens, the image light emitted from the image light source is refracted,and rays of refracted light go out to the lenticular almost in parallelto each other.

FIG. 1 is a view showing an external appearance of a conventionalFresnel lens.

In FIG. 1, 101 indicates a Fresnel lens seen on a slant. 102 indicates asectional shape of the Fresnel lens 101. 103 indicates an optical axisof the Fresnel lens 101. 104 indicates a prism portion formed for eachpitch area corresponding to one pitch length in the Fresnel lens 101.

In the manufacturing of the Fresnel lens 101, a metal mold (or a lensforming mold) is formed by rotating the mold on the optical axis 103,synthetic resin is poured into the metal mold, the synthetic resin ishardened, the metal mold is taken off from the synthetic resin, and themanufacturing of the Fresnel lens 101 is completed. On a surface of themanufactured Fresnel lens 101, a plurality of ring bands are formed in aconcentric circular shape around the optical axis 103. As is realized bylooking at the sectional shape 102 of the Fresnel lens 101, the ringbands formed in a concentric circular shape denote the plurality ofprism portions 104.

That is, the prism portions 104 of the sectional shape 102 formed in asaw-tooth shape are equally spaced at pitch intervals respectivelycorresponding to one pitch width. One pitch width of the Fresnel lens101 actually used is almost equal to 0.1 mm, and the pitch width is verysmall even though the pitch width is compared with each of minimumpixels on which an image is projected through the Fresnel lens 101. Thewhole Fresnel lens 101 functions as one convex lens. Because the prismportions 104 can be thinned, rays of light incident on the Fresnel lens101 can be changed or refracted almost without requiring a distancebetween an incident point of the ray of incident light and an outgoingpoint of a ray of outgoing light.

In the image displaying device, to shorten the depth of the imagedisplaying device, image light is often injected on the Fresnel lens 101of the screen from a direction inclined with respect to an incidentnormal of the Fresnel lens 101 as much as possible. Therefore, a thinnedtype image displaying device can be obtained.

FIG. 2 is a view showing the configuration of an image displaying devicein which a conventional Fresnel lens is applied to a screen.

A plurality of arrows indicate a plurality of rays of light. 111indicates a light emitting source (or illumination light source means)for emitting a plurality of rays of light. 112 indicates a parabolicmirror (or illumination light source means). The light emitting source111 is disposed on a focal point of the parabolic mirror 112. 113indicates a convergin glens (or converging optics means) for converginga plurality of rays of light reflected on the parabolic mirror 112. 114indicates a light bulb (or optical modulating means) formed of liquidcrystal. An intensity of each ray of light converged by the converginglens 113 is spatially changed in the light bulb 114 to modulate theconverged rays of light according to display contents written on thelight bulb 114.

115 indicates a projection optics lens (or projection optics means) forforming an image from the rays of light of which the intensities arechanged by the light bulb 114. 116 indicates a rear projection typescreen for receiving the image of the rays of light formed by theprojection optics lens 115 from the rear side and displaying the image.The rays of light spreading in the projection optics lens 115 arechanged in the screen 116 to a plurality of rays of light parallel toeach other, the image formed from the rays of light is displayed on thescreen 116, and the rays of light are diffused from the screen 116 to awide area. Therefore, the screen 116 has a function for widening a viewfield.

In the screen 116, 117 indicates a Fresnel lens described before, and118 indicates a lenticular.

In the Fresnel lens 117, the spreading rays of light sent from theprojection optics lens 115 are received on an incident plane 117A, andthe rays of light go out at a prescribed outgoing angle through a prismportion 117B arranged for each pitch area corresponding one pitch. Inshort, the Fresnel lens 117 is used to almost collimate the rays oflight spreading in the projection optics lens 115. An image is formed onthe lenticular 118 from the rays of light going out from the Fresnellens 117, and the rays of light are diffused. 119 indicates an opticalaxis. The optical axis 119 exists for the parabolic mirror 112, theconverging lens 113, the light bulb 114, the projection optics lens 115,the Fresnel lens 117 and the lenticular 118, and the optical axis 119 isperpendicular to the incident plane 117A of the Fresnel lens 117.

Next, an operation will be described below.

The light emitting source 111 disposed on a focal point of the parabolicmirror 112 can be almost regarded as a point source. Therefore, rays oflight emitted from the light emitting source 111 are reflected on theparabolic mirror 112 and goes out to the converging lens 113 as almostparallel rays of light. When the parallel rays of light are converged bythe converging lens 113 onto the light bulb 114, intensities of theconverged rays of light are spatially changed by the light bulb 114 tomodulate the converged rays of light according to display contents ofthe light bulb 114.

The rays of light intensity-modulated are projected on the rear surfaceof the screen 116 at a wide angle by the projection optics lens 115, andan image is formed from the rays of projected light. An angle betweeneach ray of light and the optical axis 119 is called a projection angle.As shown in FIG. 2, the projection angle in each pitch area differs fromthose in the other pitch areas. However, because the pitch between eachpair of prism portions 117B is considerably shorter than the lengths ofthe projection optics lens 115 and the screen 116, a plurality of raysof light incident on each prism portion 117B can be almost regarded as aplurality of parallel rays.

An angle between a normal m11 of the incident plane 117A and each ray ofincident light denotes an incident angle. Because the incident angle ofeach ray of incident light is equal to the projection angle of the rayof incident light according to the relationship of alternate-interiorangles obtained from a straight line (the incident ray) intersecting twoparallel lines (the optical axis 119 and the normal m11), the more apitch area receiving a ray of light approaches the optical axis 119, thesmaller the incident angle of the ray of light is. Also, the more apitch area receiving a ray of light is far away from the optical axis119, the larger the incident angle of the ray of light is. Inparticular, the ray of light going out to the prism portion 117B placedat each end of the screen 116 is incident on the incident plane 117A atthe maximum incident angle.

A size of the screen 116 is determined according to this maximumincident angle, or the maximum projection angle of the projection opticslens 115, and a projection distance from the projection optics lens 115to the screen 116. In contrast, in a case where the size of the screen116 is predetermined, the larger the maximum projection angle is, themore the projection distance can be shortened. Therefore, an opticalsystem having a shortened distance in the direction of the optical axis119 can be obtained, and the image displaying device can be thinned.

In the Fresnel lens 117, a plurality of rays of light are received onthe incident plane 117A at the incident angles respectively, and the rayof light goes out to the lenticular 118 at a prescribed outgoing anglethrough the prism portion 117B arranged for each pitch area. Theoutgoing angle is defined as an angle between a straight line parallelto the optical axis 119 on the Fresnel lens 117 and the ray of lightgoing out from the Fresnel lens 117. The outgoing angle is normally setto a small angle ranging from 0 degree to several degrees. In short, therays of light going out from the Fresnel lens 117 are almost parallel tothe optical axis 119 (the outgoing angle for the rays of light is set to0 degree in FIG. 2). In this case, the higher the transmissivity (aratio in power of the outgoing light to the incident light) of theFresnel lens 117 for the rays of light, the better the Fresnel lens 117.Also, the higher the transmissivity, the more the image displayed on thescreen 116 is bright.

In the lenticular 118, the rays of light are received from the prismportions 117B of the Fresnel lens 117. Also, though an image of thedisplay contents of the light bulb 114 is formed by the projectionoptics lens 115, the rays of light indicating the image are diffusedfrom the lenticular 118 in a direction (the right direction of thescreen 116 in FIG. 2) directed toward a user. The user of the imagedisplaying device views the rays of light diffused from each of aplurality of image forming points as an image. Because the rays of lightare diffused by the lenticular 118, the user can view the image whichhas the brightness required in a certain view field.

As is described above, the larger the maximum projection angle of theprojection optics lens 115, in other words, the larger the maximumincident angle of light to the Fresnel lens 117, the more the projectiondistance is shortened. Therefore, a thin type image displaying devicehaving a shortened projection distance can be provided for the user.

In cases where a size of the screen 116 is predetermined by thespecification of the screen 116, even though a large maximum projectionangle is obtained by the function of the projection optics lens 115 oranother optical unit, unless the Fresnel lens 117 receives a ray oflight corresponding to the maximum projection angle, the projectiondistance cannot be shortened. In conclusion, it is an important pointthat the Fresnel lens 117 is designed so as to set the incident angle ofa ray of light as large as possible on condition that the ray of lightgo out from the Fresnel lens 117 at high transmissivity.

Next, various principles of the conventional Fresnel lens will bedescribed below.

FIG. 3A and FIG. 3B are respectively an enlarged view showing thesectional shape of a plurality of prism portions arranged in a pluralityof pitch areas of the conventional Fresnel lens, FIG. 3A shows thesectional shape in case of a small incident angle, and FIG. 3B shows thesectional shape in case of a large incident angle. Each arrow in FIG. 3Aand FIG. 3B indicates a ray of light.

In FIG. 3A and FIG. 3B, 121 indicates a Fresnel lens. 121A indicates arefraction type prism portion formed for each pitch area of the Fresnellens 121.

121B indicates an incident plane of each refraction type prism portion121A. The incident plane 121B is formed in a flat surface shape and isperpendicular to an optical axis (not shown) of the Fresnel lens 121.121C indicates an outgoing plane of each refraction type prism portion121A. 121Z indicates an ineffective plane of each refraction type prismportion 121A. Each refraction type prism portion 121A is shaped by theincident plane 121B, the outgoing plane 121C and the ineffective plane121Z. Here, the ineffective plane 121Z does not participate with a rayof incident light or a ray of outgoing light. Also, Li indicates a rayof light incident on the incident plane 121B. Lr indicates a ray oflight reflected on the incident plane 121B. Lt indicates a ray oftransmitted light refracted on the incident plane 121B and transmittedthrough the internal of the refraction type prism portion 121A. Loindicates a ray of outgoing light refracted on the outgoing plane 121Cand going out to the air m12 indicates a normal of the incident plane121B, and m13 indicates a normal of the outgoing plane 121C.

Next, an operation will be described below.

In FIG. 3A, when a ray of incident light Li transmitted through the airhaving a refractive index of unity comes on the Fresnel lens 121 havinga refractive index of n (n>1) at a real incident angle “a” to the normalm14, the ray of incident light Li is divided on the incident plane 121Binto a ray of transmitted light Lt transmitted a tare fraction angle ofand a ray of reflected light Lr transmitted at a reflection angle of“a”. The ray of reflected light Lr causes a loss to the Fresnel lens121.

The ray of transmitted light Lt refracted on the incident plane 121B andtransmitted through the internal of the refraction type prism portion121A makes an angle of to the normal m13 and reaches the outgoing plane121C. A part of the ray of transmitted light Lt is changed to a ray ofreflected light (not shown), and the remaining part of the ray oftransmitted light Lt crosses the outgoing plane 121C and goes out as aray of outgoing light Lo at an outgoing angle of “f”.

As is described above, the ray of incident light Li incident on theFresnel lens 121 at the incident angle of “a” makes a turn in theFresnel lens 121 to a direction of an outgoing angle of “f”. Because theray of incident light Li is received on the incident plane 121B formedin a flat surface shape, the Fresnel lens 121 has a special feature inthat the ray of incident light Li is received in the Fresnel lens 121 ata high light-receiving efficiency.

In cases where the incident angle of a ray of incident light becomessmaller, the transmissivity of the incident plane is heightened, and thereflectivity of the incident plane is lowered. In contrast, in caseswhere the incident angle of a ray of light becomes larger, thetransmissivity of the incident plane is lowered, and the reflectivity ofthe incident plane is heightened. This phenomenon is well-known as anoptical theory. Accordingly, as shown in FIG. 3B, when the incidentangle “a” of a ray of light becomes larger, a ratio of the ray oftransmitted light Lt to the ray of incident light Li is decreased, and aratio of the ray of reflected light Lr to the ray of incident light Liis increased. Therefore, the transmissivity of the Fresnel lens 121 isundesirably lowered.

In short, the transmissivity of the Fresnel lens 121 depends on theincident angle. The larger the incident angle “a”, the more thetransmissivity is lowered. Also, in cases where the Fresnel lens 121 isapplied to a screen of which the size is predetermined, the thinning ofthe image displaying device is undesirably restricted due to thelimitation of the maximum incident angle.

In another type of Fresnel lens having there fraction type prismportion, as is described below, the structure on the incident side ofthere fraction type prism portion 121A shown in FIG. 3A and FIG. 3B ischanged to that on an outgoing side, and the structure on the outgoingside of the refraction type prism portion 121A shown in FIG. 3A and FIG.3B is changed to that on an incident side.

FIG. 4A and FIG. 4B are en larged views respectively showing thesectional shape of a plurality of prism portions arranged in a pluralityof pitch areas of another type conventional Fresnel lens, FIG. 4A showsthe sectional shape in case of a small incident angle, and FIG. 4B showsthe sectional shape in case of a large incident angle. An arrow in eachof FIG. 4A and FIG. 4B indicates a ray of light.

In FIG. 4A and FIG. 4B, 131 indicates a Fresnel lens. 131A indicates arefraction type prism portion formed for each pitch area of the Fresnellens 131.

131B indicates an incident plane of each refraction type prism portion131A. 131C indicates an outgoing plane of each refraction type prismportion 131A. 131Z indicates an ineffective plane of each refractiontype prism portion 131A. Each refraction type prism portion 131A isshaped by the incident plane 131B, the outgoing plane 131C and theineffective plane 131Z. The incident plane 131B is formed in a flatsurface shape and is perpendicular to an optical axis (not shown) of theFresnel lens 131. Though rays of light are received on the ineffectiveplane 131Z, the ineffective plane 131Z does not participate in thegoing-out of a ray of light from the outgoing plane 131C. Also, Liindicates a ray of light incident on the incident plane 131B. Lrindicates a ray of light reflected on the incident plane 131B. Ltindicates a ray of transmitted light refracted on the incident plane131B and transmitted through the internal of the refraction type prismportion 131A. Lo indicates a ray of outgoing light refracted on theoutgoing plane 131C and going out to the air. Le indicates a ray ofineffective light received on the ineffective plane 131Z. m14 indicatesa normal of the outgoing plane 131C, and m15 indicates a normal of theincident plane 131B.

Next, an operation will be described below.

In FIG. 4A, when a ray of incident light Li transmitted through the airhaving a refractive index of unity comes on the Fresnel lens 131 havinga refractive index of n (n>1) at an incident angle of “a” to the normalm14, the ray of incident light Li is incident on the incident plane 131Bat a real incident angle of “b” to the normal m15, and the ray ofincident light Li is divided on the incident plane 131B into a ray oftransmitted light Lt transmitted at a refraction angle of and a ray ofreflected light Lr transmitted at a reflection angle of “b”. The ray ofreflected light Lr causes a loss to the Fresnel lens 131.

The ray of transmitted light Lt refracted on the incident plane 131B andtransmitted through the refraction type prism portion 131A makes anangle of to the normal m14 and reaches the outgoing plane 131C. Apart ofthe ray of transmitted light Lt is changed to a ray of reflected light(not shown), and the remaining part of the ray of transmitted light Ltcrosses the outgoing plane 131C and goes out as a ray of outgoing lightLo at an outgoing angle of “f”.

Also, because the ray of ineffective light Le received on theineffective plane 131Z goes out from the outgoing plane 131C at an angledifferent from the outgoing angle of “f”, the ray of ineffective lightLe causes a loss to the Fresnel lens 131.

As is described above, the ray of incident light Li incident on theFresnel lens 131 at the incident angle of “a” makes a turn in theFresnel lens 131 to a direction of the outgoing angle of “f”. Becausethe Fresnel lens 131 has the outgoing plane 131C formed in a flatsurface shape, in cases where the Fresnel lens 131 is applied to ascreen, the Fresnel lens 131 has a special feature in that a lenticularcan be integrally formed with the outgoing plane 131C.

However, for the same reason as that in the Fresnel lens 121, as shownin FIG. 4B, in cases where the incident angle of “a” becomes larger, aratio of the ray of reflected light Lr to the ray of incident light Liis undesirably increased, and an area (an area of slash marks in each ofFIG. 4A and FIG. 4B) of the ray of ineffective light received on theineffective plane 131Z is undesirably enlarged.

Therefore, in the same manner as in the Fresnel lens 121, thetransmissivity of the Fresnel lens 131 depends on the incident angle.And, the larger the incident angle, the more the transmissivity islowered.

As is described above, in cases where the incident angle in the Fresnellens 131 having the refraction type prism portions is increased, thetransmissivity of the Fresnel lens 131 is undesirably lowered. Also, incases where the Fresnel lens 131 is applied to a screen of which thesize is predetermined, the thinning of the image displaying device isundesirably restricted due to the lowering of the transmissivity of theFresnel lens 131.

To remedy the above-described defects in the conventional Fresnel lenshaving the refraction type prism portions and to obtain a hightransmissivity of the Fresnel lens in case of a large incident angle,another conventional Fresnel lens will be described below.

FIG. 5A and FIG. 5B are enlarged views respectively showing thesectional shape of a plurality of prism portions arranged in a pluralityof pitch areas of another type conventional Fresnel lens, FIG. 5A showsthe sectional shape in case of a large incident angle, and FIG. 5B showsthe sectional shape in case of a small incident angle. Each arrow inFIG. 5A and FIG. 5B indicates a ray of light.

In FIG. 5A and FIG. 5B, 141 indicates a Fresnel lens. 141A indicates atotal reflection type prism portion formed for each pitch area of theFresnel lens 141.

141B indicates an incident plane of each total reflection type prismportion 141A, 141C indicates a total reflection plane of each totalreflection type prism portion 141A, 141D indicates an outgoing plane ofeach total reflection type prism portion 141A. Each total reflectiontype prism portion 141A is shaped by the incident plane 141B, the totalreflection plane 141C and the outgoing plane 141D. The outgoing plane141D is formed in a flat surf ace shape and is perpendicular to anoptical axis (not shown) of the Fresnel lens 141. In a case where a rayof light transmitted through a high refractive index type medium isincident on a plane between the high refractive index type medium and alow refractive index type medium at a large incident angle larger than acritical angle, the ray of light is totally reflected on the plane. Thisphenomenon is used in the reflection performed on the total reflectionplane 141C.

Also, Li indicates a ray of light incident on the incident plane 141B.Lt1 indicates a ray of transmitted light refracted on the incident plane141B and transmitted through the total reflection plane 141C. Lt2indicates a ray of transmitted light totally reflected on the totalreflection plane 141C and transmitted to the outgoing plane 141D. Loindicates a ray of outgoing light refracted on the outgoing plane 141Dand going out to the air. Le indicates a ray of ineffective lightreceived on the incident plane 141B. m16 indicates a normal of theoutgoing plane 141D, m17 indicates a normal of the incident plane 141B,and m18 indicates a normal of the total reflection plane 141C.

Next, an operation will be described below.

In FIG. 5A, when a ray of incident light Li transmitted through the airhaving a refractive index of unity comes on the Fresnel lens 141 havinga refractive index of n (n>1) at an incident angle of “a” to the normalm16, the ray of incident light Li is incident on the incident plane 141Bat a real incident angle of “b” to the normal m17, and the ray ofincident light Li is divided on the incident plane 141B into a ray oftransmitted light Lt1 transmitted at a refraction angle of and a ray ofreflected light (not shown). The ray of reflected light generated on theincident plane 141B causes a loss to the Fresnel lens 141.

The ray of transmitted light Lt1 refracted on the incident plane 141Band transmitted through the total reflection type prism portion 141Areaches the total reflection plane 141C at an angle which is made to thenormal m18 and is larger than the critical angle, the ray of transmittedlight Lt1 is totally reflected on the total reflection plane 141C, andthe ray of transmitted light Lt1 totally reflected is transmitted as theray of transmitted light Lt2. Because an optical path of the ray oftransmitted light Lt1 is bent by using the phenomenon of the totalreflection, no ray of light is transmitted through or goes out from thetotal reflection plane 141C. Therefore, loss in the transmitted lightLt1 is hardly generated on the total reflection plane 141C.

The ray of transmitted light Lt2 to tally reflected on the totalreflection plane 141C is transmitted at an angle of to the normal m16and reaches the outgoing plane 141D. A part of the ray of transmittedlight Lt2 is changed to a ray of reflected light (not shown), and theremaining part of the ray of transmitted light Lt2 is transmittedthrough the outgoing plane 141D and goes out as a ray of outgoing lightLo at an outgoing angle of “f” (0 degree in FIG. SA).

Because an optical path is bent in each of the Fresnel lens 121 havingthe refraction type prism portions 121A and the Fresnel lens 131 havingthe refraction type prism portions 131A according to the refractionphenomenon, it is required that the ray of incident light Li is receivedin each of the Fresnel lenses 121 and 131 at a large real incident angleof “a” or “b” to bend the optical path to a considerable degree.Therefore, a ratio of the ray of reflected light Lr to the ray ofincident light Li on each of the incident planes 121B and 131B isincreased, and the transmissivity of each of the Fresnel lenses 121 and131 for the ray of incident light Li is undesirably decreased.

In contrast, in the Fresnel lens 141 having the total reflection typeprism portions 141A, because the optical path is bent according to thetotal reflection phenomenon, a degree of the bending of the optical pathbased on the refraction phenomenon can be reduced. Therefore, the ray ofincident light Li can be incident on the incident plane 141 Bat a smallreal incident angle of “b”, the increase of there flectivity of theFresnel lens 141 can be suppressed, and high transmissivity of theFresnel lens 141 can be obtained.

As is described above, differently from the Fresnel lenses 121 and 131,high transmissivity can be obtained for the large incident angle in theFresnel lens 141 having the total reflection type prism portions 141A.

However, as shown in FIG. 5B, in cases where the incident angle of “a”is decreased in the Fresnel lens 141, the ray of incident light Lireceived on the incident plane 141B is decreased, a ratio of the rays oftransmitted light Lt2 totally reflected on the total reflection plane141C to the rays of incident light Li is decreased, and rays ofineffective light Le (placed in an area of slash marks in FIG. 5B) areinevitably generated.

Though each ray of ineffective light Le is transmitted through theinside of the total reflection type prism portion 141A, the totalreflection of the ray of ineffective light Le on the total reflectionplane 141C is not performed. Therefore, the rays of ineffective light Lecause a loss to the Fresnel lens 141. In other words, the transmissivityof the Fresnel lens 141 for the rays of incident light Li depends on theincident angle. Therefore, though the transmissivity of the Fresnel lens141 for the high incident angle of “a” can be heightened, thetransmissivity of the Fresnel lens 141 for the low incident angle of “a”is undesirably decreased.

Because each conventional Fresnel lens has the above-describedconfiguration, a problem has arisen that the transmissivity of theconventional Fresnel lens for the rays of incident light Li considerablydepends on the incident angle.

Therefore, in each conventional Fresnel lens, a part of image lightprojected on a screen on a slant at an angle larger than a maximumprojection angle cannot be deflected to a desired direction, and thetransmissivity of the conventional Fresnel lens for the rays of incidentlight Li is low.

Here, a conventional Fresnel lens will be briefly described below oncemore.

FIG. 6 is a view, partially in cross-section, of a conventional Fresnellens on which image light is projected on a slant.

In FIG. 6, 100 indicates a conventional Fresnel lens in which aplurality of refraction type prism portions are arranged in a pluralityof pitch areas. 100 a indicates an incident plane disposed on a lightincident side of the Fresnel lens 100. 100 b indicates an in effectiveplane disposed on a light incident side of the Fresnel lens 100. 100 cindicates an outgoing plane disposed on a light outgoing side of theFresnel lens 100. R1 in indicates a light flux incident on the incidentplane 100 a. R2 in indicates a light flux incident on the ineffectiveplane 100 b.

The Fresnel lens 100 shown in FIG. 6 has a plurality of very smallrefraction type prism portions each of which denotes a unit of prismportion. In each refraction type prism portion, alight flux R1 inincident on the incident plane 100 a on a slant is deflected and goesout as a light flux R1 out through the outgoing plane 100 c.

However, alight flux R2 i incident on the ineffective plane 100 bdifferent from the incident plane 100 a does not go out in a desireddirection but goes out as stray light. Therefore, the light flux R2 icannot be effectively used, and the transmissivity of the Fresnel lens100 is low.

A Fresnel lens having a plurality of total reflection type prismportions is proposed as a means for solving the above-described problem,and rays of light are deflected in the Fresnel lens according to thetotal reflection.

For example, a Fresnel lens having a plurality of refraction type prismportions and a plurality of total reflection type prism portionsalternately disposed is proposed in Published Unexamined Japanese PatentApplication No. 52601 of 1986. Also, a Fresnel lens having a pluralityof prism portions is proposed in Published Unexamined Japanese PatentApplication No. 19837 of 1987, and a refraction using portion and atotal reflection using portion are disposed in each prism portion.However, in the Fresnel lens disclosed in the Published UnexaminedJapanese Patent Application No. 52601 of 1986, a refraction type prismportion additionally exists in an area in which the refraction typeprism portion does not effectively function, and a total reflection typeprism portion additionally exists in an area in which the totalreflection type prism portion does not effectively function. Therefore,a problem has arisen that a large amount of light does not still go outin a desired direction.

In contrast, in the Fresnel lens disclosed in the Published UnexaminedJapanese Patent Application No. 19837 of 1987, the shape of the Fresnellens in section is formed in a polygonal shape. Therefore, in caseswhere a lens forming mold used to form the Fresnel lens is manufactured,a cutting tool having a specific shape is required, and it is difficultto manufacture the lens forming mold. In its turn, it is difficult tomanufacture the Fresnel lens.

Also, in cases where each conventional Fresnel lens is applied to a rearprojection type screen, a problem has arisen that the brightness of animage displayed on the screen is not uniformly set.

In detail, in cases where a Fresnel lens having refraction type prismportions is applied to the screen, the Fresnel lens cannot effectivelyfunction in case of a large projection angle. Therefore, the brightnessof an image displayed in a peripheral area of the screen is undesirablylowered, and the thinning of the image displaying device is restricted.

Also, in cases where a Fresnel lens having total reflection type prismportions is applied to the screen, the Fresnel lens cannot effectivelyfunction in case of a small projection angle. Therefore, the brightnessof an image in an area of the screen placed in the neighborhood of anoptical axis is undesirably lowered.

The present invention is provided to solve the above-described problems,and the object of the present invention is to provide a Fresnel lens inwhich the dependence of transmissivity on an incident angle is lowered.

Also, the present invention is to provide a screen, in which unevennessof the brightness of an image is suppressed in a range from a smallprojection angle to a large projection angle, and to provide an imagedisplaying device to which the screen is applied.

In addition, the present invention is to provide a lens forming moldmanufacturing method, in which a lens forming mold of the Fresnel lensis manufactured, and a lens manufacturing method using the lens formingold manufacturing method.

DISCLOSURE OF THE INVENTION

A Fresnel lens according to the present invention includes a pitch areahaving a hybrid type prism portion which has both a refraction typeprism portion for making a ray of first incident light having aprescribed incident angle go out according to a first refractionphenomenon and a second refraction phenomenon as a ray of first outgoinglight having a prescribed outgoing angle and a total reflection prismportion for making a ray of second incident light having the prescribedincident angle go out according to a third refraction phenomenon, atotal reflection phenomenon and a fourth refraction phenomenon as a rayof second outgoing light parallel to the ray of first outgoing light.

Therefore, a Fresnel lens having high transmissivity can be obtainedwhile lowering the dependence of transmissivity on an incident angle.

A Fresnel lens according to the present invention further includesanother pitch area having the hybrid type prism portion or a pluralityof other pitch areas having the hybrid type prism portions respectively,and a ratio of an area occupied by the refraction type prism portion toan area occupied by the hybrid type prism portion in each pitch areadiffers from ratios in the other pitch areas.

Therefore, the transmissivity in the Fresnel lens can be improved. AFresnel lens according to the present invention includes a plurality ofpitch areas respectively having a hybrid type prism portion which hasboth a refraction type prism portion and a total reflection prismportion integrally formed with each other. The refraction type prismportion of each pitch area has a sectional shape formed by a firstincident plane for changing a ray of first incident light incident at aprescribed incident angle to a ray of first transmitted light accordingto a first refraction phenomenon, a plane-shaped outgoing plane forchanging the ray of first transmitted light obtained on the firstincident plane to a ray of first outgoing light having a prescribedoutgoing angle according to a second refraction phenomenon, and anineffective plane connecting with the first incident plane and anadjacent pitch area. The total reflection type prism portion of eachpitch area has a sectional shape formed by a second incident plane forchanging a ray of second incident light incident at the prescribedincident angle to a ray of second transmitted light according to a thirdrefraction phenomenon, a total reflection plane for changing the ray ofsecond transmitted light obtained on the second incident plane to a rayof third transmitted light parallel to the ray of first transmittedlight according to a total reflection phenomenon, and the outgoing planeof the refraction type prism portion. The ray of third transmitted lightobtained in the total reflection plane is changed to a ray of secondoutgoing light having the prescribed outgoing angle according to afourth refraction phenomenon on the outgoing plane, and a portion of theray of second incident light not changed to the ray of third transmittedlight is received as the ray of first incident light. Therefore, aFresnel lens having high transmissivity can be obtained while loweringthe dependence of transmissivity on an incident angle.

In the Fresnel lens according to the present invention, the secondincident plane of each pitch area is formed in a sectional shape so asto make the second incident plane conceal the ineffective plane of thehybrid type prism portion arranged in an adjacent pitch from a view seenin a direction of a ray of ineffective light incident on the ineffectiveplane, and the total reflection plane of each pitch area is formed in asecond incident plane compensating shape so as to compensate for thesectional shape of the second incident plane.

Therefore, a light receiving efficiency of the Fresnel lens can beheightened while decreasing an ineffective area.

In the Fresnel lens according to the present invention, a small incidentangle region is determined according to a characteristic changing angleat which transmissivity of the hybrid type prism portion is equal tothat of the refraction type prism portion, and the refraction type prismportion is arranged in each of pitch areas placed in the small incidentangle region.

Therefore, characteristics of transmissivity in the small incident angleregion can be improved.

In the Fresnel lens according to the present invention, a small incidentangle region is determined according to a characteristic changing angleat which transmissivity of the hybrid type prism portion is equal tothat of the refraction type prism portion, and the refraction type prismportion is arranged in each of pitch areas placed in the small incidentangle region.

Therefore, characteristics of transmissivity in the small incident angleregion can be improved.

In the Fresnel lens according to the present invention, a mixing ratioof the refraction type prism portion to the hybrid type prism portion isincreased with the decrease of the incident angle in each of pitch areascorresponding to a characteristic changing region neighboring to thecharacteristic changing angle.

Therefore, characteristics of transmissivity in the small incident angleregion can be improved, and the transmissivity in the characteristicchanging region neighboring to the characteristic changing angle can besmoothly changed.

In the Fresnel lens according to the present invention, a mixing ratioof the refraction type prism portion to the hybrid type prism portion isincreased with the decrease of the incident angle in each of pitch areascorresponding to a characteristic changing region neighboring to thecharacteristic changing angle.

Therefore, characteristics of transmissivity in the small incident angleregion can be improved, and the transmissivity in the characteristicchanging region neighboring to the characteristic changing angle can besmoothly changed.

In the Fresnel lens according to the present invention, an intermediaryprism portion is arranged as one hybrid type prism portion in each ofpitch areas corresponding to a characteristic changing regionneighboring to the characteristic changing angle, an area of the secondincident plane of the intermediary prism portion is slightly decreasedwith the decrease of the incident angle, and an area of the firstincident plane of the intermediary prism portion is slightly increasedwith the decrease of the incident angle.

Therefore, characteristics of transmissivity in the small incident angleregion can be improved, and a change of the transmissivity at thecharacteristic changing angle can be smoothed.

In the Fresnel lens according to the present invention, an intermediaryprism portion is arranged as one hybrid type prism portion in each ofpitch areas corresponding to a characteristic changing regionneighboring to the characteristic changing angle, an area of the secondincident plane of the intermediary prism portion is slightly decreasedwith the decrease of the incident angle, and an area of the firstincident plane of the intermediary prism portion is slightly increasedwith the decrease of the incident angle.

Therefore, characteristics of transmissivity in the small incident angleregion can be improved, and a change of the transmissivity at thecharacteristic changing angle can be smoothed.

In the Fresnel lens according to the present invention, a top bladeangle between the second incident plane and the total reflection planeis set to a most-acute angle in a range in which an angle between thesecond incident plane and the outgoing plane is not obtuse.

Therefore, transmissivity of the Fresnel lens can be further improved.

In the Fresnel lens according to the present invention, the top bladeangle is set to an angle larger than the most-acute angle in a smallincident angle region corresponding to incident angles smaller than aspecific incident angle at which transmissivity corresponding to the topblade angle set to the most-acute angle is equal to transmissivitycorresponding to the top blade angle different from the most-acuteangle.

Therefore, a Fresnel lens having high transmissivity at all incidentangles can be obtained.

In the Fresnel lens according to the present invention, the prescribedoutgoing angle is set to a value larger than zero degree in each ofpitch areas corresponding to incident angles at which transmissivity ofthe hybrid type prism portions is decreased.

Therefore, transmissivity of the Fresnel lens can be further improved.

In the Fresnel lens according to the present invention, the Fresnel lensis cut in a rectangular shape so as to have four sides, a boundary ringband of the Fresnel lens intersects only one side nearest to an opticalaxis among the four sides of the Fresnel lens, the outgoing angle is setso as to make the ray of first outgoing light and the ray of secondoutgoing light going out on a lens periphery side of the boundary ringband be parallel to the optical axis, and the outgoing angle of the rayof first outgoing light and the ray of second outgoing light going outon an optical axis side of the boundary ring band is set to a valuelarger than that corresponding to the ray of first outgoing light andthe ray of second outgoing light going out in parallel to the opticalaxis.

Therefore, in cases where the Fresnel lens is applied to a screen of animage displaying device having a multiple-structure,the uniformity ofluminance on the screen can be improved.

In the Fresnel lens according to the present invention, each refractiontype prism portion has a thin-film light absorbing layer on theineffective layer, and the thin-film light absorbing layer absorbslight.

Therefore, a ray of ineffective light expected to be received on theineffective plane and be changed to stray light in the inside of theFresnel lens can be absorbed in the thin-film light absorbing layer, andghosts generated on the screen can be reduced.

The Fresnel lens according to the present invention further includes astray light absorbing plate which is arranged on the outgoing plane andhas a plurality of light transmitting layers and a plurality of lightabsorbing layers alternately layered almost in parallel to an opticalaxis of the Fresnel lens. A ray of light is transmitted through eachlight transmitting layer, and light is absorbed in each light absorbinglayer.

Therefore, stray light generated in the inside of the Fresnel lens canbe absorbed, and ghosts generated on the screen can be reduced.

In the Fresnel lens according to the present invention, the stray lightabsorbing plate arranged on the outgoing plane is integrally formed withthe Fresnel lens.

Therefore, the ghosts can be reduced by using a small number ofconstituent parts.

In the Fresnel lens according to the present invention, the lighttransmitting layers and the light absorbing layers are layered in aconcentric circular shape while centering around the optical axis of theFresnel lens.

Therefore, a reduction efficiency of the ghosts can be maximized.

In the Fresnel lens according to the present invention, the lighttransmitting layers and the light absorbing layers are layered in adirection almost in parallel to each other.

Therefore, the stray light absorbing plate can be easily manufactured,and a manufacturing cost can be reduced.

The Fresnel lens according to the present invention further includes alight absorbing plate, arranged on the outgoing layer, for absorbinglight.

Therefore, stray light can be absorbed by using a simple structure, andghosts generated on a screen can be reduced.

In the Fresnel lens according to the present invention, the hybrid typeprism portions are formed while having a pitch margin between each pairof pitch areas adjacent to each other.

Therefore, the total reflection plane can be formed in a shapedetermined in the designing, and the optical performance of the Fresnellens can be guaranteed.

The Fresnel lens according to the present invention further includes agroup of pitch areas in which a plurality of dummy prism portions aresuccessively arranged. A height of each dummy prism portion in anoptical axis direction is set not to have relation to the reception oflight.

Therefore, a rapid disappearance and occurrence of a manufacturing erroroccurring by the change of the shape of the prism portion can besuppressed, and a rapid change of the optical performance such astransmissivity can be relieved.

A screen according to the present invention, includes the Fresnel lens,and an image forming and diffusing means for receiving the ray ofoutgoing light, to which display contents are added, from the Fresnellens, forming an image from the ray of outgoing light and diffusing theimage.

Therefore, unevenness of the brightness of an image can be suppressed,and a screen applicable in a range from a small projection angle to alarge projection angle can be obtained.

A screen according to the present invention, includes the Fresnel lensand an image forming and diffusing means for receiving the ray ofoutgoing light, to which display contents are added, from the Fresnellens, forming an image from the ray of outgoing light and diffusing theimage.

Therefore, unevenness of the brightness of an image can be suppressed,and a screen applicable in a range from a small projection angle to alarge projection angle can be obtained.

In the screen according to the present invention, the image forming anddiffusing means is arranged on the outgoing plane to be integrallyformed with the Fresnel lens.

Therefore, a screen manufactured by using a reduced number ofconstituent parts can be provided.

In the screen according to the present invention, the image forming anddif fusing means is arranged on the outgoing plane to be integrallyformed with the Fresnel lens.

Therefore, a screen manufactured by using a reduced number ofconstituent parts can be provided.

An image displaying device according to the present invention includesthe screen, illumination light source means for emitting a plurality ofrays of light almost parallel to each other, converging optics means forconverging the rays of light emitted from the illumination light sourcemeans, optical modulating means for spatially changing intensities ofthe rays of light converged by the converging optics means so as tomodulate the rays of light according to the display contents, andprojection optics means for rejecting the rays of light modulated by theoptical modulating means into the screen.

Therefore, an image displaying device having an improved brightness ofan image can be obtained.

An image displaying device according to the present invention includesthe screen, illumination light source means for emitting a plurality ofrays of light almost parallel to each other, converging optics means forconverging the rays of light emitted from the illumination light sourcemeans, optical modulating means for spatially changing intensities ofthe rays of light converged by the converging optics means so as tomodulate the rays of light according to the display contents, andprojection optics means for projecting the rays of light modulated bythe optical modulating means onto the screen.

Therefore, an image displaying device having an improved brightness ofan image can be obtained.

A Fresnel lens according to the present invention includes a pluralityof total reflection type prism portions which respectively have asubsidiary unit-prism portion in a part of a second incident plane onwhich a ray of light expected not to be totally reflected on a totalreflection plane is incident. A refraction type prism portion having afirst incident plane on which the ray of incident light is refracted tobe deflected in a desired direction is set as the subsidiary unit-prismportion.

Therefore, the subsidiary unit-prism portion functions as a lens for aray of light for which the total reflection type prism portion does noteffectively function, and the transmissivity of the Fresnel lens can beimproved.

In the Fresnel lens according to the present invention, a plane obtainedby extending the first incident plane of each subsidiary unit-prismportion is placed in a position shifted from the total reflection planetoward a light outgoing side in a range of the corresponding totalreflection type prism portion.

Therefore, a Fresnel lens possible to be easily manufactured can beprovided.

In the Fresnel lens according to the present invention, a ratio of eachsubsidiary unit-prism portion to the corresponding second incident planediffers from those of the other subsidiary unit-prism portions.

Therefore, each subsidiary unit-prism portion can be formed in anoptimum shape in correspondence to an incident angle of a light flux,and a Fresnel lens having high transmissivity can be obtained.

In the Fresnel lens according to the present invention, a ratio of eachsubsidiary unit-prism portion to the corresponding second incident planediffers from those of the other subsidiary unit-prism portions.

Therefore, each subsidiary unit-prism portion can be formed in anoptimum shape in correspondence to an incident angle of a light flux,and a Fresnel lens having high transmissivity can be obtained.

A Fresnel lens according to the present invention, includes a pluralityof refraction type prism portions which respectively have a subsidiaryunit-prism portion, in which a ray of light expected to be incident onan ineffective plane of another adjacent refraction type prism portionplaced on a Fresnel periphery side is received, on a first incidentplane. A total reflection type prism portion has both a second incidentplane, on which a ray of light is received, and a total reflectionplane, on which the ray of light received on the second incident planeis totally reflected to be deflected in a desired direction, and is setas the subsidiary unit-prism portion.

Therefore, the subsidiary unit-prism portion functions as a lens for aray of light for which the refractive type prism portion does noteffectively function, and the transmissivity of the Fresnel lens can beimproved.

In the Fresnel lens according to the present invention, a plane obtainedby extending the second incident plane of each subsidiary unit-prismportion is placed in a position shifted from the ineffective planetoward a light outgoing side in a range of the corresponding refractiontype prism portion.

Therefore, a Fresnel lens possible to be easily manufactured can beprovided.

In the Fresnel lens according to the present invention, a ratio of eachsubsidiary unit-prism portion to the corresponding first incident planediffers from those of the other subsidiary unit-prism portions.Therefore, each subsidiary unit-prism portion can be formed in anoptimum shape in correspondence to an incident angle of a light flux,and a Fresnel lens having high transmissivity can be obtained.

In the Fresnel lens according to the present invention, a ratio of eachsubsidiary unit-prism portion to the corresponding first incident planediffers from those of the other subsidiary unit-prism portions.

Therefore, each subsidiary unit-prism portion can be formed in anoptimum shape in correspondence to an incident angle of a light flux,and a Fresnel lens having high transmissivity can be obtained.

A Fresnel lens according to the present invention, includes a firstregion in which the Fresnel lens, is arranged, and a second region inwhich a plurality of refraction type prism portions respectively havingboth a first incident plane, on which a ray of incident light isrefracted to be deflected in a desired direction, and an ineffectiveplane different from the first incident plane are arranged on a lightincident side, wherein each refraction type prism portion has asubsidiary unit-prism portion arranged on the first incident plane, aray of light expected to be incident on the ineffective plane of anotheradjacent refraction type prism portion placed on a Fresnel peripheryside is received in the subsidiary unit-prism portion, and thesubsidiary unit-prism portion functions as a total reflection type prismportion having both a second incident plane, on which a ray of light isreceived, and a total reflection plane on which the ray of lightreceived on the second incident plane is totally reflected to bedeflected in the desired direction.

Therefore, an optimum shape of each unit-prism portion can be selectedfrom the first region or the second region in correspondence to anincident angle of a light flux and be formed, and a Fresnel lens havinghigh transmissivity can be obtained.

In the Fresnel lens according to the present invention, a ratio of thesubsidiary unit-prism portion to the corresponding second incident planein the first region is increased as the subsidiary unit-prism portionapproaches a boundary between the first region and the second region,the ratio of the subsidiary unit-prism portion to the correspondingsecond incident plane in the first region is decreased as the subsidiaryunit-prism portion is far a way from the boundary, a ratio of thesubsidiary unit-prism portion to the corresponding first incident planein the second region is increased as the subsidiary unit-prism portionapproaches the boundary, and the ratio of the subsidiary unit-prismportion to the corresponding first incident plane in the second regionis decreased as the subsidiary unit-prism portion is far away from theboundary.

Therefore, the ratios of the subsidiary unit-prism portion are increasedas the subsidiary unit-prism portion approaches the boundary in whichthe subsidiary unit-prism portion effectively functions, and a Fresnellens having high transmissivity can be obtained.

In the Fresnel lens according to the present invention, a second Fresnellens different from the Fresnel lens arranged on a plane of the lightincident side is arranged on a plane of a light outgoing side of theFresnel lens.

Therefore, the Fresnel lens arranged on the light incident side and theFresnel lens arranged on the light outgoing side are cooperated, and aFresnel lens having transmissivity further heightened can be obtained.

In the Fresnel lens according to the present invention, a second Fresnellens different from the Fresnel lens arranged on a plane of a lightincident side is arranged on a plane of a light outgoing side of theFresnel lens.

Therefore, the Fresnel lens arranged on the light incident side and theFresnel lens arranged on the light outgoing side are cooperated, and aFresnel lens having transmissivity further heightened can be obtained.

A screen according to the present invention, includes the Fresnel lens,and light diffusing means, arranged on a plane of a light outgoing sideof the Fresnel lens, for diffusing the rays of light going out from theFresnel lens.

Therefore, a screen applicable in a range from a small projection angleto a large projection angle can be obtained while decreasing the numberof constituent parts and suppressing unevenness of the brightness of animage.

A screen according to the present invention, includes the Fresnel lens,and light diffusing means, arranged on a plane of a light outgoing sideof the Fresnel lens, for diffusing the rays of light going out from theFresnel lens.

Therefore, a screen applicable in a range from a small projection angleto a large projection angle can be obtained while decreasing the numberof constituent parts and suppressing unevenness of the brightness of animage.

A screen according to the present invention, includes the Fresnel lens,and light diffusing means, arranged on a light outgoing side of theFresnel lens, for diffusing the rays of light going out from the Fresnellens.

Therefore, a screen applicable in a range from a small projection angleto a large projection angle can be obtained while suppressing unevennessof the brightness of an image.

A screen according to the present invention, includes the Fresnel lens,and light diffusing means, arranged on a light outgoing side of theFresnel lens, for diffusing the rays of light going out from the Fresnellens.

Therefore, a screen applicable in a range from a small projection angleto a large projection angle can be obtained while suppressing unevennessof the brightness of an image.

An image displaying device according to the present invention, includesthe screen, an image light source for emitting a plurality of rays ofimage light, and projection optics means for projecting the rays ofimage light emitted from the image light source on to the screen.

Therefore, an image displaying device displaying an image of an improvedbrightness can be provided.

An image displaying device according to the present invention, includesthe screen, an image light source for emitting a plurality of rays ofimage light, and projection optics means for projecting the rays ofimage light emitted from the image light source on to the screen.

Therefore, an image displaying device displaying an image of an improvedbrightness can be provided.

An image displaying device according to the present invention, includesthe screen, an image light source for emitting a plurality of rays ofimage light, and projection optics means for projecting the rays ofimage light emitted from the image light source on to the screen.

Therefore, an image displaying device displaying an image of an improvedbrightness can be provided.

An image displaying device according to the present invention, includesthe screen, an image light source for emitting a plurality of rays ofimage light, and projection optics means for projecting the rays ofimage light emitted from the image light source on to the screen.

Therefore, an image displaying device displaying an image of an improvedbrightness can be provided.

A method of manufacturing a lens forming mold according to the presentinvention, includes a main unit-prism portion cutting step of cutting alens forming mold in a reversed shape of a refractive type prism portionof a cutting pitch area by using a cutting tool, and a subordinateunit-prism portion cutting step of cutting the lens forming mold in areversed shape of a total reflection type prism portion of the cuttingpitch area by using the cutting tool on condition that a plane obtainedby extending an incident plane in the reversed shape of the totalreflection type prism portion intersects a trough line placed betweenthe cutting pitch area and another cutting area adjacent to the cuttingpitch area on a Fresnel center side or pass through an area shifted fromthe trough line toward a light outgoing side. The combination of themain unit-prism portion cutting step and the subordinate unit-prismportion cutting step is repeatedly performed by a prescribed numberequal to the number of cutting pitch areas.

Therefore, a lens forming mold can be easily manufactured by using anormal cutting tool, and the precision in the manufacturing of the lensforming mold can be improved.

A method of manufacturing a lens forming mold according to the presentinvention, includes a main unit-prism portion cutting step of cutting alens forming mold in a reversed shape of a total reflection type prismportion of a cutting pitch area by using a cutting tool, and asubordinate unit-prism portion cutting step of cutting the lens formingmold in a reversed shape of a refractive type prism portion of thecutting pitch area by using the cutting tool on condition that a planeobtained by extending a first incident plane in the reversed shape ofthe refractive type prism portion intersects a trough line placedbetween the cutting pitch area and another cutting area adjacent to thecutting pitch area on a Fresnel periphery side or pass through an areashifted from the trough line toward a light outgoing side, wherein thecombination of the main unit-prism portion cutting step and thesubordinate unit-prism portion cutting step is repeatedly performed by aprescribed number equal to the number of cutting pitch areas.

Therefore, a lens forming mold can be easily manufactured by using anormal cutting tool, and the precision in the manufacturing of the lensforming mold can be improved.

The method of manufacturing a lens forming mold according to the presentinvention, further includes a pitch margin setting step for setting apitch margin for each cutting pitch area before the subordinateunit-prism portion cutting step in cases where the lens forming mold iscut in a cut performing direction from the Fresnel periphery side to aFresnel center side in the order of the refractive type prism portionand the total reflection type prism portion. The lens forming mold iscut by shifting a cutting start position toward the cut performingdirection by the pitch margin to form a reversed shape of the totalreflection type prism portion in the subordinate unit-prism portioncutting step for each cutting pitch area.

Therefore, in cases where the lens forming mold is cut in the reversedshape of the refractive type prism portion, the distortion of the lensforming mold occurring in a tip portion on the trough line placedbetween the total reflection type prism portions for each pitch area canbe prevented, the lens forming mold can be formed in a shape determinedin the designing, and the optical performance of the Fresnel lensmanufactured by using the lens forming mold can be guaranteed.

The method of manufacturing a lens forming mold according to the presentinvention, further includes a pitch margin setting step for setting apitch margin for each cutting pitch area before the subordinateunit-prism portion cutting step in cases where the lens forming mold iscut in a cut performing direction from a Fresnel center side to theFresnel periphery side in the order of the total reflection type prismportion and the refractive type prism portion, wherein the lens formingmold is cut by shifting a cutting start position toward the cutperforming direction by the pitch margin to form the reversed shape ofthe refractive type prism portion in the subordinate unit-prism portioncutting step for each cutting pitch area.

Therefore, in cases where the lens forming mold is cut in the reversedshape of the total reflect ion type prism portion, the distortion of thelens forming mold occurring in a tip portion on the trough line placedbetween the refractive type prism portions for each pitch area can beprevented, the lens forming mold can be formed in a shape determined inthe designing, and the optical performance of the Fresnel lensmanufactured by using the lens forming mold can be guaranteed.

A method of manufacturing a lens forming mold according to the presentinvention, further includes the step of successively cutting the lensforming mold in a reversed shape of a plurality of dummy prism portionsrespectively having a height in an optical axis direction not related tothe reception of light for a group of pitch areas.

Therefore, a rapid disappearance and occurrence of a manufacturing erroroccurring by the change of the shape of the prism portion can besuppressed, and a rapid change of the optical performance such astransmissivity in a Fresnel lens can be relieved.

A method of manufacturing a lens according to the present invention,includes the steps of pouring resin into a lens forming moldmanufactured in the method of manufacturing a lens forming moldhardening the resin, and taking off the lens forming mold from thehardened resin to form a lens.

Therefore, a Fresnel lens having high precision can be easilymanufactured.

A method of manufacturing a lens according to the present invention,includes the steps of pouring resin into a lens forming moldmanufactured in the method of manufacturing a lens forming moldhardening the resin, and taking off the lens forming mold from thehardened resin to form a lens.

Therefore, a Fresnel lens having high precision can be easilymanufactured.

A method of manufacturing a lens according to the present invention,includes the steps of pouring resin in to a lens forming moldmanufactured in the method of manufacturing a lens forming moldhardening the resin, and taking off the lens forming mold from thehardened resin to form a lens.

Therefore, a Fresnel lens having high precision can be easilymanufactured.

A method of manufacturing a lens according to the present invention,includes the steps of pouring resin in to a lens forming moldmanufactured in the method of manufacturing a lens forming moldhardening the resin, and taking off the lens forming mold from thehardened resin to form a lens.

Therefore, a Fresnel lens having high precision can be easilymanufactured.

A method of manufacturing a lens according to the present invention,includes the steps of pouring resin into a lens forming moldmanufactured in the method of manufacturing a lens forming moldhardening the resin, and taking off the lens forming mold from thehardened resin to form a lens.

Therefore, a Fresnel lens having high precision can be easilymanufactured.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a view showing an external appearance of a conventionalFresnel lens.

FIG. 2 is a view showing the configuration of an image displaying devicein which the conventional Fresnel lens is applied to a screen.

FIG. 3A and FIG. 3B are enlarged views respectively showing a sectionalshape of a plurality of prism portions arranged in a plurality of pitchareas of the conventional Fresnel lens.

FIG. 4A and FIG. 4B are enlarged views respectively showing a sectionalshape of a plurality of prism portions arranged in a plurality of pitchareas of another conventional Fresnel lens.

FIG. 5A and FIG. 5B are enlarged views respectively showing a sectionalshape of a plurality of prism portions arranged in a plurality of pitchareas of another conventional Fresnel lens.

FIG. 6 is a view of a conventional Fresnel lens on which image light isprojected on a slant.

FIG. 7 is an enlarged view showing a sectional shape of a Fresnel lensin one pitch area according to a first embodiment of the presentinvention.

FIG. 8 is a view showing changes of transmissivity in a refraction typeprism portion, a total reflection type prism portion and a hybrid typeprism portion with respect to incident angle.

FIG. 9 is a view explaining rays of ineffective light in the Fresnellens shown in the first embodiment.

FIG. 10 is an enlarged view of a sectional shape of a Fresnel lens inone pitch area according to a second embodiment of the presentinvention.

FIG. 11 is a view showing the comparison between the transmissivity ofthe hybrid type prism portion 2 shown in the first embodiment and thetransmissivity of a refraction type prism portion shown in the priorart.

FIG. 12 is an enlarged view of a sectional shape of a Fresnel lensaccording to a third embodiment of the present invention in a pluralityof pitch areas.

FIG. 13 is an enlarged view of a sectional shape of another Fresnel lensaccording to the third embodiment of the present invention in aplurality of pitch areas.

FIG. 14 is an enlarged view of a sectional shape of another Fresnel lensaccording to the third embodiment of the present invention in aplurality of pitch areas.

FIG. 15 is a view showing the transmissivity of the hybrid type prismportion in case of top blade angles set to 45 degrees, 40 degrees and 35degrees.

FIG. 16 is a view showing the transmissivity of the hybrid type prismportion in case of outgoing angles “f” set to 0 degree, 3 degrees and 5degrees.

FIG. 17A and FIG. 17B are respectively a view showing the configurationof an image displaying device in which the Fresnel lens is applied to ascreen.

FIG. 18A, FIG. 18B and FIG. 18C are views explaining a method ofoptimizing the outgoing angle of a ray of outgoing light.

FIG. 19 is a view explaining a method of optimizing the outgoing angleof a ray of outgoing light.

FIG. 20 is a view of the whole structure of a rear projection type imagedisplaying device according to a fifth embodiment of the presentinvention.

FIG. 21 is a view of the image displaying device shown in FIG. 20 seenfrom one side.

FIG. 22 is a view showing a sectional shape of the Fresnel lens.

FIG. 23A, FIG. 23B and FIG. 23C are views explaining a total reflectiontype prism portion U1 and a refraction type prism portion U2.

FIG. 24A, FIG. 24B and FIG. 24C are views explaining features of a lensforming mold used for the manufacturing of the Fresnel lens 51.

FIG. 25A, FIG. 25B and FIG. 25C are views explaining features of a lensforming mold used for the manufacturing of the Fresnel lens 51.

FIG. 26 is a flow chart showing a method of manufacturing a lens formingmold according to the fifth embodiment of the present invention.

FIG. 27A, FIG. 27B, FIG. 27C and FIG. 27D are views showing steps of acutting work for the lens forming mold C using a cutting tool B.

FIG. 28A, FIG. 28B, FIG. 28C and FIG. 28D are views showing steps ofanother cutting work for the lens forming mold C using the cutting toolB.

FIG. 29 is a view showing the relationship among a radius of a Fresnellens measured from the Fresnel center, a ratio of an area occupied bythe total reflection type prism portion U1 and a ratio of an areaoccupied by the refraction type prism portion U2 to the area of theFresnel lens 51.

FIG. 30 is a view showing the configuration of a Fresnel lens 110according to the prior art.

FIG. 31 is a view showing a lens ratio of a total reflection type prismportion to the Fresnel lens 110 shown in FIG. 30.

FIG. 32 is a view showing the transmissivity of the Fresnel lens 51based on the fifth embodiment and the transmissivity of the Fresnel lens110 based on the prior art.

FIG. 33A to FIG. 33F are views explaining distortion occurring in aplurality of manufacturing steps of the lens forming mold.

FIG. 34 is a flow chart showing a method of manufacturing a lens formingmold according to a sixth embodiment of the present invention.

FIG. 35A to FIG. 35F are views showing the shape of the lens formingmold cut step by step according to the method of manufacturing a lensforming mold shown in FIG. 34.

FIG. 36A and FIG. 36B are views explaining the configuration andoperation of a Fresnel lens having no dummy prism portion.

FIG. 37A and FIG. 37B are views explaining the configuration andoperation of a Fresnel lens having dummy prism portions.

FIG. 38A and FIG. 38B are views explaining the difference between theFresnel lens of FIG. 36A and the Fresnel lens of FIG. 37A.

FIG. 39 is a view showing a sectional shape of a Fresnel lens accordingto a seventh embodiment of the present invention.

FIG. 40 is a view showing a sectional shape of another Fresnel lensaccording to the seventh embodiment of the present invention.

FIG. 41A and FIG. 41B are views respectively showing an example of alayered structure of light transmitting layers and light absorbinglayers.

FIG. 42 is a view showing a sectional shape of another Fresnel lensaccording to the seventh embodiment of the present invention.

BEST MODE FOR CARRYING OUT THE INVENTION

Hereinafter, the best mode for carrying out the present invention willnow be described with reference to the accompanying drawings to explainthe present invention in more detail.

Embodiment 1

FIG. 7 is an enlarged view showing a sectional shape of a Fresnel lensin one pitch area according to a first embodiment of the presentinvention. Each arrow denotes a ray of light. Here, a sectional shapedenotes a shape of a cutting plane of a plurality of prism portions ofthe Fresnel lens obtained in a case where the Fresnel lens is cut alonga plane which includes an optical axis of the Fresnel lens.

In FIG. 7, 1 indicates a Fresnel lens according to a first embodiment. 2indicates a hybrid type prism portion which is formed for each pitcharea corresponding to one pitch of the Fresnel lens 1. 3A indicates arefraction type prism portion. 4A indicates a total reflection typeprism portion. 5 indicates an outgoing plane of the hybrid type prismportion 2. The outgoing plane 5 is formed in a flat surface shape and isperpendicular to an optical axis (not shown) of the Fresnel lens 1. Therefraction type prism portions 3A and the total reflection type prismportions 4A have the outgoing plane 5 in common. Each hybrid type prismportion 2 comprises the refraction type prism portion 3A and thecorresponding total reflection type prism portion 4A.

In each refraction type prism portion 3A, 3B indicates an incident plane(or a first incident plane) of the refraction type prism portion 3A, and3Z indicates an ineffective plane. A shape of each refraction type prismportion 3A is formed by the incident plane 3B, the outgoing plane 5 andthe ineffective plane 3Z. Though a ray of light is received on theineffective plane 3Z, the ineffective plane 3Z does not participate inthe going-out of a ray of light from the outgoing plane S.

In each total reflection type prism portions 4A, 4B indicates anincident plane (or a second incident plane) of the total reflection typeprism portions 4A, and 4C indicates a total reflection plane. A shape ofeach total reflection type prism portion 4A is formed by the incidentplane 4B, the outgoing plane 5 and the total reflection plane 4C. Aphenomenon of the total reflection is used for the total reflectionplane 4C, and a ray of light transmitted through a high refractive indextype medium and being incident on a plane between the high refractiveindex type medium and a low refractive index type medium at an incidentangle larger than a critical angle is totally reflected on the plane.Any ray of light directed from the air to the total reflection plane 4Cis not incident on the total reflection plane 4C because the ray oflight is interrupted by the incident plane 4B.

Li1 denotes a ray of incident light (or a ray of first incident light)transmitted through the air and being incident on the incident plane 3B.Lt1 denotes a ray of transmitted light (or a ray of first transmittedlight) transmitted to the outgoing plane 5 due to the refraction (or afirst refraction phenomenon) of the ray of incident light Li1 on theincident plane 3B. Lo1 denotes a ray of outgoing light (or a ray offirst outgoing light) going out to the air due to the refraction (or asecond refraction phenomenon) of the ray of transmitted light Lt1 on theoutgoing plane 5.

Li2 denotes a ray of incident light (or a ray of second incident light)transmitted through the air and being incident on the incident plane 4B.Lt2 denotes a ray of transmitted light (or a ray of second transmittedlight) transmitted to the total reflection plane 4C due to therefraction (or a third refraction phenomenon) of the ray of incidentlight Li2 on the incident plane 4B. Lt3 denotes a ray of transmittedlight (or a ray of third transmitted light) transmitted to the outgoingplane 5 due to the total reflection (or a total reflection phenomenon)of the ray of transmitted light Lt2 on the total reflection plane 4C.Lo2 denotes a ray of outgoing light (or a ray of second outgoing light)going out to the air due to the refraction (or a fourth refractionphenomenon) of the ray of transmitted light Lt3 on the outgoing plane 5.

Also, m1 indicates a normal of the incident plane 3B, m2 indicates anormal of the incident plane 4B, m3 indicates a normal of the totalreflection plane 4C, and m4 indicates a normal of the outgoing plane 5.

Next, an operation will be described below.

In FIG. 7, when a ray of incident light Li1 and a ray of incident lightLi2 transmitted through the air having a refractive index of unity comeon the Fresnel lens 1 having a refractive index of n (n >1) at anincident angle “a”, the ray of incident light Li1 is received on theincident plane 3B of the refraction type prism portion 3A, and the rayof incident light Li2 is received on the incident plane 4B of the totalreflection type prism portion 4A.

Initially, the ray of incident light Li1 received on the incident plane3B is described.

The ray of incident light Li1 is incident on the incident plane 3B at areal incident angle b1 to the normal m1 and is divided into a ray oftransmitted light Lt1 transmitted at a refraction angle. 1 to the normalm1 and a ray of reflected light (not shown). The ray of reflected lighton the incident plane 3B causes a loss to the Fresnel lens 1.

The ray of transmitted light Lt1 refracted on the incident plane 3B istransmitted through the refraction type prism portion 3A and reaches theoutgoing plane 5 at an angle to the normal m4. A part of the transmittedlight Lt1 is changed to a ray of reflected light (not shown), and theremaining part of the transmitted light Lt1 goes out from the outgoingplane 5 at an outgoing angle “f” to the normal m4 as a ray of outgoinglight Lo1.

In contrast, the ray of incident light Li2 received on the incidentplane 4B is incident on the incident plane 4B at a real incident angleb2 to the normal m2 and is divided into a ray of transmitted light Lt2transmitted at a refraction angle 2 to the normal m2 and a ray ofreflected light (not shown). The ray of reflected light on the incidentplane 4B causes a loss to the Fresnel lens 1.

The ray of transmitted light Lt2 refracted on the incident plane 4B istransmitted through the total reflection type prism portion 4A andreaches the total reflection plane 4C at an angle of 90−d degrees to thenormal m3. The angle of 90−d degrees is larger than a critical angle ofthe total reflection plane 4C. Thereafter, the ray of transmitted lightLt2 is totally reflected on the total reflection plane 4C and is changedto a ray of transmitted light Lt3. In this case, the total reflectionplane 4C is designed in advance so as to make the ray of transmittedlight Lt3 be parallel to the ray of transmitted light Lt1. Because anoptical path of the transmitted light Lt2 is bent by using thephenomenon of the total reflection, no ray of light goes out from thetotal reflection plane 4C. Therefore, rays of light on the totalreflection plane 4C hardly cause a loss to the Fresnel lens 1.

The ray of transmitted light Lt3 totally reflected on the totalreflection plane 4C reaches the outgoing plane 5 at an angle to thenormal m4. A part of the transmitted light Lt3 is changed to a ray ofreflected light (not shown), and the remaining part of the transmittedlight Lt3 goes out from the outgoing plane 5 at the outgoing angle “f”to the normal m4 as a ray of outgoing light Lo2. Because the transmittedlight Lt1 is parallel to the transmitted light Lt3, the ray of outgoinglight Lo1 and the ray of outgoing light Lo2 are output in parallel toeach other.

As is described above, the Fresnel lens 1 comprises the hybrid typeprism portions 2 respectively obtained by combining one refraction typeprism portion 3A and one total reflection type prism portion 4A. Inother words, each hybrid type prism portion 2 is obtained by reshaping aportion of one refraction type prism portion 3A to one total reflectiontype prism portion 4A so as to receive the rays of the ineffective lightLe (placed in an area of slash marks) described with reference to FIG.5B on the incident plane 3B, and the Fresnel lens 1 has the hybrid typeprism portions 2 arranged in a plurality of pitch areas respectivelycorresponding to one pitch. The ineffective lights Le are kind of like apart of the rays of light Li2 each of which is incident on the incidentplane 4B and is not changed to the ray of transmitted light Lt3 due tono total reflection on the total reflection plane 4C, and theineffective lights Le causing a loss in the total reflection type prismportion 4A are substantially received in the refraction type prismportion 3A.

In cases where the incident angle “a” and the outgoing angle “f” to theoutgoing plane 5 formed in a flat surface shape are determined, an anglebetween the outgoing plane 5 and the incident plane 3B is determinedaccording to the law of refraction. Also, in addition to the incidentangle “a” and the outgoing angle “f”, in cases where a top blade anglebetween the total reflection plane 4C and the incident plane 4B isdetermined, an angle between the outgoing plane 5 and the totalreflection plane 4C is determined according to the law of refraction andthe law of total reflection. The top blade angle is set to an optimumvalue with respect to the incident angle so as to obtain the hybrid typeprism portion 2 having a high transmissivity. Also, an angle between theoutgoing plane 5 and the ineffective plane 3Z is set to a value (90degrees in FIG. 7) at which a forming-mold (or a lens forming mold) canbe taken off in the manufacturing of the Fresnel lens 1.

Because the Fresnel lens 1 comprises the hybrid type prism portions 2respectively obtained by combining the refraction type prism portion 3Ahaving the high transmissivity for the small incident angle “a” and thetotal reflection type prism portion 4A having the high transmissivityfor the large incident angle “a”, the Fresnel lens 1 can have anexcellent transmissivity in a wide range of the incident angle “a”.

To realize the effect of the first embodiment, the transmissivity willbe analyzed below with reference to FIG. 7.

The transmissivity TX of the refraction type prism portion 3A and thetransmissivity TY of the total reflection type prism portion 4A areexpressed according to equations (1) and (2) respectively.

<Transmissivity TX of Refraction Type Prism Portion 3A>

TX=[tan(·−d)/{tan(·−d)−tan(·+·)}]×{1−than (·)×tan(a)}×[1−{(n−1)/(n+1)}²]×[1−0.5×(PX ² +QX ²)]  (1)

Here,

PX=tan[a+·−sin⁻¹{(1/n)×sin(a+·)}]÷tan[a+·+sin⁻¹{(1/n)×sin(a+·)}]

and

QX=tan[a+·−sin ⁻¹{(1/n)×sin(a+·)}]÷sin[a+·+sin⁻¹{(1/n)×sin(a+·)}]

are satisfied.

<Transmissivity TY of Total Reflection Type Prism Portion 4A>

TY=[tan(·)/{tan(·)−tan(·+·)}−tan(·−d)/{tan(·−d)−tan(·+·)}]×{1−than(·+·)×tan(a)}×[1−{(n−1)/(n+1)}²]×[1−0.5×(PY² +Qy ²)]  (2)

Here,

 PY=tan[b−sin¹{(1/n)×sin(b)}]÷tan[b+sin⁻¹{(1/n)×sin(b)}] and

QY=tan[b−sin¹{(1/n)×sin(b)}]÷sin[b+sin⁻¹{(1/n)×sin(b)}]

are satisfied.

A transmissivity Tall of the hybrid type prism portion 2 is obtained asa sum of the transmissivity TX and the transmissivity TY and isexpressed according to an equation (3).

<Transmissivity Tall of Hybrid Type Prism Portion 2>

Tall=TX+TY  (3)

Changes of the transmissivity TX, the transmissivity TY and thetransmissivity Tall with respect to the incident angle “a” are shown inFIG. 8 according to the equations (1), (2) and (3). The outgoing angle“f”=0 degree, the top blade angle=45 degrees and the refraction anglen=1.5 are set as calculation conditions.

In FIG. 8, the X-axis indicates the incident angle “a” in degree, andthe Y-axis indicates the transmissivity in percentage (%). Also, thetransmissivity TX of the refraction type prism portion 3A is indicatedby a broken line, the transmissivity TY of the total reflection typeprism portion 4A is indicated by a dot-dash line, and the transmissivityTall of the hybrid type prism portion 2 is indicated by a solid line.

In FIG. 8, the transmissivity TY of the total reflection type prismportion 4A is equal to or higher than 90% in a region of the incidentangle “a” equal to or higher than 40 degrees. Also, as the incidentangle “a” is decreased from 40 degrees, the transmissivity TY is rapidlydecreased. Therefore, it is realized that the transmissivity TY of thetotal reflection type prism portion 4A depends on the incident angle.

In contrast to the characteristic of the transmissivity TY, as theincident angle “a” is decreased, the transmissivity TX of there fractiontype prism portion 3A is increased. Therefore, the transmissivity TX ofthe refraction type prism portion 3A depending on the incident angle isindicated.

Because the hybrid type prism portion 2 comprises the refraction typeprism portion 3A and the total reflection type prism portion 4A havingthe incident angle dependences different from each other, as shown bythe transmissivity Tall in FIG. 8, the transmissivity Tall is equal toor higher than 90% in a region of the incident angle “a” higher than 40degrees, and the refraction type prism portion 3A compensates for thedecrease of the transmissivity TY of the total reflection type prismportion 4A in a region of the incident angle “a” equal to or lower than40 degrees. Therefore, the transmissivity Tall is equal to or higherthan almost 60% in a region of the incident angle “a” from 0 to 90degrees.

As is described above, in the first embodiment, the ray of incidentlight Li2 of the incident angle “a” is received at the real incidentangle b2 and is refracted as the ray of transmitted light Lt2 on theincident plane 4A, the ray of transmitted light Lt2 is received at anangle larger than the critical angle and is totally reflected as the rayof transmitted light Lt3 on the total reflection plane 4C, and the rayof transmitted light Lt3 is refracted on the outgoing plane 5 and goesout at the outgoing angle “f” as the ray of outgoing light Lo2. Thetotal reflection type prism portion 4A has the sectional shape formed bythe incident plane 4A, the total reflection plane 4C and the outgoingplane 5. Apart of the rays of ineffective light functioning asineffective light in the total reflection type prism portion 4A arereceived at the real incident angle b1 as the rays of transmitted lightLi1 and are refracted on the incident plane 3B as the rays oftransmitted light Lt1 parallel to the ray of transmitted light Lt3. Therefraction type prism portion 3A has the sectional shape formed by theoutgoing plane 5 of the total reflection type prism portion 4A, theincident plane 3B and the ineffective plane 3Z intersecting with boththe outgoing plane 5 and the incident plane 3B. The Fresnel lens 1 hasthe hybrid type prism portion 2 for each pitch area, and each hybridtype prism portion 2 is composed of the total reflection type prismportion 4A and there fraction type prism portion 3A. Accordingly, theFresnel lens 1 having the high transmissivity and theconsiderably-reduced incident angle dependence can be obtained.

Here, it is not required to arrange the hybrid type prism portions 2 inall pitch areas, and it is applicable that the hybrid type prismportions 2 be used for the Fresnel lens 1 with the conventionalrefraction type prism portions 131A and the conventional totalreflection type prism portions 141A. For example, the Fresnel lens 1 ofall pitch areas is divided into three groups of pitch areascorresponding to three types of incident angles different from eachother, the conventional refraction type prism portions 131A are arrangedin the first group of pitch areas, the hybrid type prism portions 2 arearranged in the second group of pitch-areas, and the conventional totalreflection type prism portions 141A are arranged in the third group ofpitch areas. In this case, because the Fresnel lens has the group of thehybrid type prism portions 2 and the group of the conventional prismportions, one group of prism portions optimum to the incident angle canbe selected. Therefore, the incident angle dependence of the Fresnellens having the high transmissivity can be further reduced, and an imagedisplaying device displaying a bright image on the whole image plane canbe provided.

Embodiment 2

In the Fresnel lens 1 of the first embodiment, there are rays ofineffective light received on the ineffective plane 3Z. Because each rayof ineffective light does not go out from the outgoing plane 5 at theoutgoing angle “f”, the ray of ineffective light causes a loss in theFresnel lens 1. In a second embodiment, a method of reducing rays ofineffective light will be described.

FIG. 9 is a view explaining rays of ineffective light occurring in theFresnel lens of the first embodiment. Each arrow indicates a ray oflight. The constituent elements, which are the same as those shown inFIG. 7, are indicated by the same reference numerals as those of theconstituent elements shown in FIG. 7.

In FIG. 9, Lie indicates each of a plurality of rays of ineffectivelight received on the ineffective plane 3Z or an ineffective plane 3Zarranged on another pitch area adjacent to that of the ineffective plane3Z. Each area E1 indicated by slash marks denotes an ineffective areathrough which a flux of ineffective light Lie is transmitted. Ltedenotes a ray of transmitted light obtained from one ray of ineffectivelight Lie which is refracted on the ineffective plane 3Z and istransmitted through the Fresnel lens 1. Loe denotes a ray of outgoinglight obtained from the ray of transmitted light Lte which is refractedon the outgoing plane 5 and goes out to the air at an outgoing angle“f1” (·f).

As is realized by viewing FIG. 9, each ray of ineffective light Lie isrefracted on the ineffective plane 3Z and is changed to the ray oftransmitted light Lte, the ray of transmitted light Lte is refracted onthe outgoing plane 5 and is changed to the ray of outgoing light Loe atan outgoing angle “f 1” to the outgoing plane 5. Therefore, because theray of ineffective light Lie transmitted through the ineffective area E1and received on the ineffective plane 3Z does not go out at the outgoingangle “f”, the ray of ineffective light Lie causes a loss in the Fresnellens 1.

To prevent this problem in the second embodiment, an amount of rays ofineffective light is reduced by using a Fresnel lens which has a prismportion of a sectional shape shown in FIG. 10 for each pitch area.

FIG. 10 is an enlarged view of a sectional shape of a Fresnel lens inone pitch area according to the second embodiment of the presentinvention. Each arrow indicates aray of light. The constituent elements,which are the same as those shown in FIG. 7 or FIG. 9, are indicated bythe same reference numerals as those of the constituent elements shownin FIG. 7 or FIG. 9.

In FIG. 10, 6 indicates a Fresnel lens according to the secondembodiment. 7 indicates a hybrid type prism portion of the Fresnel lens6. The hybrid type prism portion 7 has the refraction type prism portion3A in the same manner as the hybrid type prism portion 2 of the firstembodiment.

8A indicates a total reflection type prism portion. Each hybrid typeprism portion 7 is formed by one total reflection type prism portion 8Aand one refraction type prism portion 3A. 8B indicates an incident plane(or a second incident plane) of the total reflection type prism portion8A. 8C indicates a total reflection plane of the total reflection typeprism portion 8A. 9 indicates an outgoing plane of the hybrid type prismportion 7. The outgoing plane 9 is formed in a flat surface shape. 3Z-1indicates an ineffective plane of another refraction type prism portionformed in a pitch area adjacent to the total reflection type prismportion 8A. 8B-2 indicates an incident plane of another total reflectiontype prism portion formed in a pitch area adjacent to there fractiontype prism portion 3A. Also, E2 indicates an ineffective area throughwhich a flux of the ineffective light Lie is transmitted. E3 indicatesan effective area obtained by removing the ineffective area E2 from theineffective area E1. In short, E1=E2+E3 is satisfied.

A sectional shape of the incident plane 8B is formed so as to make theincident plane 8B conceal a part of the ineffective plane 3Z-1 of theadjacent pitch area from a view seen in a propagation direction of theray of ineffective light Lie. Therefore, any ray of light transmittedthrough the effective area E3 among rays of light transmitted throughthe ineffective area E1 shown in FIG. 9 is not received on theineffective plane 3Z-1 but is received on the incident plane 8B as a rayof incident light Li2. As a result, it can be realized from FIG. 10 thatthe ineffective area E1 is narrowed to the ineffective area E2.

Because the sectional shape of the incident plane 8B is formed in acurved line shape to intercept the ray of ineffective light Lie directedto the ineffective plane 3Z-1 of the adjacent pitch area, refractionangles on the incident plane 8B for rays of incident light Li2 passingthrough optical paths different from each other differ from each other.Therefore, a sectional shape of the total reflection plane 8C is formedin a curved line shape (or a second incident plane compensating shape)so as to totally reflect rays of transmitted light Lt2 corresponding tothe refract ion angles different from each other as rays of transmittedlight Lt3 and so as to make the rays of transmitted light Lt3 beparallel to the ray of transmitted light Lt1 refracted on the incidentplane 3B of the refraction type prism portion 3A.

Next, an operation will be described below.

Because the ray of light transmitted through the refraction type prismportion 3A is the same as that of the first embodiment, the descriptionof the ray of light transmitted through the refraction type prismportion 3A is omitted.

A ray of transmitted light Lt2 refracted on the incident plane 8B istotally reflected on the total reflection plane 8C and is transmitted tothe outgoing plane 9 as a ray of transmitted light Lt3. Because theshape of the total reflection plane 8C is designed so as to make the rayof transmitted light Lt3, which is obtained by to tally reflecting theray of transmitted light Lt2, be parallel to the ray of transmittedlight Lt1 transmitted from the incident plane 3B, the ray of transmittedlight Lt3 is refracted on the outgoing plane 9 in the same manner as theray of transmitted light Lt1 and goes out as a ray of outgoing light Lo2at an outgoing angle “f”.

Therefore, because a part of the rays of ineffective light Lie, whichare placed in the effective area E3 and are expected to be received onthe ineffective plane 3Z-1 of the pitch area adjacent to the totalreflection type prism portion 8A, are received on the incident plane 8Bas rays of incident light Li2, the ineffective area E1 can be narrowedto the ineffective area E2, and a light receiving efficiency of thehybrid type prism portion 7 can be heightened.

The ineffective plane 3Z of the hybrid type prism portion 7 is concealedfrom the rays of ineffective light Lie by the incident plane 8B-2 of thepitch area adjacent to the refraction type prism portion 3A when theineffective plane 3Z is seen in a propagation direction of the rays ofineffective light Lie. The ineffective planes 3Z in the other pitchareas are also covered with the incident plane in the same manner, theineffective areas El are narrowed over the entire Fresnel lens 6, and alight receiving efficiency of the whole Fresnel lens 6 can be improved.

As is described above, in the second embodiment, the incident plane 8Bconceals the ineffective plane 3Z-1 of the pitch area adjacent to thetotal reflection type prism portion 8A when the ineffective plane 3Z-1is seen in a propagation direction of the rays of ineffective light Lie,all rays of transmitted light Lt2 refracted on the incident plane 8B aretotally reflected and are changed to the rays of transmitted light Lt3parallel to the rays of transmitted light Lt1 on the total reflectionplane 8C, and each total reflection type prism portion 8A has theincident plane 8B and the total reflection plane 8C. Accordingly, theineffective area E1 can be narrowed, and a light receiving efficiency ofthe Fresnel lens 6 can be heightened.

Here, because the manufacturing of the Fresnel lens 6 is completed bytaking off a forming mold (or a lens forming mold) from hardenedsynthetic resin, the sectional shape of the total reflection type prismportions 8A is formed so as to be possible to take off the forming mold.

Also, the second embodiment is not restricted to the Fresnel lens havingthe hybrid type prism portions, and the second embodiment can be appliedto a Fresnel lens having the conventional total reflection type prismportions.

Embodiment 3

In the first embodiment, the hybrid type prism portions 2 respectivelyhaving both the refraction type prism portion 3A and the totalreflection type prism portion 4A are reshaped to obtain the Fresnel lens1, and the transmissivity of the hybrid type prism portion shown in FIG.8 is obtained. However, the transmissivity in a region of the smallincident angles is slightly low as compared with that in a region of thelarge incident angles. In a third embodiment, a method of improving thetransmissivity in a region of the small incident angles will bedescribed.

FIG. 11 is a view showing the comparison between the transmissivity ofthe hybrid type prism portion 2 shown in the first embodiment and thetransmissivity of the refraction type prism portion 131A shown in theprior art.

In FIG. 11, in the same manner as in FIG. 8, the X-axis indicates theincident angle “a” in degree, and the Y-axis indicates thetransmissivity in percentage (%). The transmissivity of the hybrid typeprism portion 2 is indicated by a solid line, and the transmissivity ofthe refraction type prism portion 131A is indicated by a dot-dash line.

Because the Fresnel lens 131 described with reference to FIG. 4 has anexcellent transmissivity in a region of small incident angles, as isrealized in FIG. 11, the transmissivity of the refraction type prismportion 131A is high in a region of incident angles smaller than acharacteristic changing angle “a0” as compared with the transmissivityof the hybrid type prism portion 2. The characteristic changing angle“a0” is defined as an incident angle at which the transmissivity of thehybrid type prism portion 2 agrees with the transmissivity of therefraction type prism portion 131A.

Therefore, in a third embodiment, the refraction type prism portion 131Ais applied to the Fresnel lens 1 having the hybrid type prism portion 2,and the transmissivity of a Fresnel lens in a region of small incidentangles is improved.

FIG. 12 is an enlarged view of a sectional shape of a Fresnel lens in aplurality of pitch areas according to the third embodiment of thepresent invention. Each arrow denotes a ray of light.

In FIG. 12, 10 indicates a Fresnel lens according to the thirdembodiment. 11A and 11B indicate hybrid type prism portions of theFresnel lens 1 described in the first embodiment respectively. 12A and12B indicate refraction type prism portions of the Fresnel lens 131described in the prior art respectively. 13 indicates an outgoing planeof the Fresnel lens 10. The outgoing plane 13 is formed in a flatsurface shape. m5 indicates a normal of the outgoing plane 13.

Li3, Li4, Li5 and Li6 indicate a ray of incident light transmitted tothe prism portion 11A at an incident angle “a1” to the normal m5, a rayof incident light transmitted to the prism portion 11B at an incidentangle “a2” to the normal m5, a ray of incident light transmitted to theprism portion 12A at an incident angle “a3” to the normal m5 and a rayof incident light transmitted to the prism portion 12B at an incidentangle “a4” to the normal m5 respectively.

The incident angles “a1”, “a2”, “a3” and “a4” and the characteristicchanging angle “a0” satisfy the relationship of al>a2.a0>a3>a4 (oral>a2>a0.a3>a4). Therefore, a most-end portion of the

Fresnel lens 10 is placed in an upper direction (or above in FIG. 12) ofthe prism portion 1A, and an optical axis of the Fresnel lens 10 isplaced in a lower direction (or below in FIG. 12) of the prism portion12B. The hybrid type prism portion 111A or 11B is arranged in each ofpitch areas ranging from the most-end portion of the Fresnel lens 10 tothe hybrid type prism portion 11B, and the refraction type prism portion12A or 12B is arranged in each of pitch areas ranging from therefraction type prism portion 12A to the optical axis of the Fresnellens 10.

In other words, in the Fresnel lens 10 shown in FIG. 12, the hybrid typeprism portions 11A and 11B are applied to the pitch areas satisfying therelationship a.a0 (or a>a0) for the incident angle “a”, and therefraction type prism portions 12A and 12B are applied to the pitchareas satisfying the relationship a0>a (or a0.a) for the incident angle“a”. The characteristic changing angle “a0” denotes a changing point of

the sectional shape of the prism portion, the hybrid type prism portions11A and 11B are arranged in the pitch areas placed in the region ofsmall incident angles smaller than (or equal to or smaller than) thecharacteristic changing angle “a0”, and the refraction type prismportions 12A and 12B are arranged in the pitch areas placed in theregion of large incident angles equal to or larger than (or larger than)the characteristic changing angle “a0”. Therefore, the transmissivity ofthe Fresnel lens 10 agrees with the transmissivity of the Fresnel lens131 shown in FIG. 11 in a region of incident angles smaller than thecharacteristic changing angle “a0”, and the transmissivity of theFresnel lens 10 agrees with the transmissivity of the Fresnel lens 1shown in FIG. 11 in a region of incident angles larger than thecharacteristic changing angle “a0”. Accordingly, the transmissivity ofthe Fresnel lens 10 in a region of the small incident angles can beheightened as compared with the Fresnel lens 1 of the first embodiment.

Also, tow smoothly change the transmissivity of the Fresnel lens 10 inthe neighborhood of the characteristic changing angle “a0”, a followingimprovement is preferred.

FIG. 13 is an enlarged view of a sectional shape of another Fresnel lensin a plurality of pitch areas according to the third embodiment of thepresent invention. Each arrow denotes a ray of light.

In FIG. 13, 14 indicates another Fresnel lens according to the thirdembodiment. 15C, 15D, 15E, 15F, 15G and 15H respectively indicate hybridtype prism portions of the Fresnel lens described in the firstembodiment. 16C, 16D, 16E and 16F respectively indicate refraction typeprism portions of the Fresnel lens 131 described in the prior art. 17indicates an outgoing plane of the Fresnel lens 14. The outgoing plane17 is formed in a flat surface shape. m6 indicates a normal of theoutgoing plane 17.

Li7 indicates a ray of incident light transmitted to the prism portion15C at an incident angle “a5” to the normal m6, Li8 indicates a ray ofincident light transmitted to the prism portion 15D at an incident angle“a6” to the normal m6, Li9 indicates a ray of incident light transmittedto the prism portion 15E at an incident angle “a7” to the normal m6,Li10 indicates a ray of incident light transmitted to the prism portion16C at an incident angle “a8” to the normal m6, Li11 indicates a ray ofincident light transmitted to the prism portion 15F at an incident angle“a9” to the normal m6, Li12 indicates a ray of incident lighttransmitted to the prism portion 15G at an incident angle “a10” to thenormal m6, Li13 indicates a ray of incident light transmitted to theprism portion 16D at an incident angle “all” to the normal m6, Li14indicates a ray of incident light transmitted to the prism portion 15Hat an incident angle “a12” to the normal m6, Li15 indicates a ray ofincident light transmitted to the prism portion 16E at an incident angle“a13” to the normal m6, and Li16 indicates a ray of incident lighttransmitted to the prism portion 16F at an incident angle “a14” to thenormal m6.

The incident angles satisfy the relationship a5>a6>- ->a13>a14.Therefore, a most-end portion of the Fresnel lens 14 is placed in anupper direction (or above in FIG. 13) of the hybrid type prism portion15C, and an optical axis of the Fresnel lens 14 is placed in a lowerdirection (or below in FIG. 13) of the refraction type prism portion16F.

The hybrid type prism portion is arranged in each of pitch areas rangingfrom the most-end portion of the Fresnel lens 14 to the hybrid typeprism portion 15C, and the refraction type prism portion is arranged ineach of pitch areas ranging from the refraction type prism portion 16Fto the optical axis of the Fresnel lens 14.

In the Fresnel lens 14 shown in FIG. 13, as the incident angle “a” isdecreased in pitch areas corresponding to incident angles (or acharacteristic changing region) neighboring to the characteristicchanging angle “a0”, a ratio (or a mixing ratio) of the number ofrefraction type prism portions to the number of hybrid type prismportions is increased step by step.

For example, it is presumed that the characteristic changing angle “a0”is placed between the incident angle “a10” and the incident angle “all”.In this case, as shown in FIG. 13, the prism portions corresponding toincident angles neighboring to the characteristic changing angle “a0”are arranged in the mixing ratio of 1 to 3 in the pitch areascorresponding to the hybrid type prism portions 15C to 15E and therefraction type prism portion 16C, are arranged in the mixing ratio of 1to 2 in the pitch areas corresponding to the hybrid type prism portions15F, 15G and the refraction type prism portion 16D and are arranged inthe mixing ratio of 1 to 1 in the pitch areas corresponding to thehybrid type prism portion 15H and the refraction type prism portion 16E.

Therefore, the hybrid type prism portions 15C to 15H and there fractiontype prism portions 16C to 16F are mixed in the pitch areas of thecharacteristic changing region corresponding to the incident anglesneighboring to the characteristic changing angle “a0”, and the mixingratio of the number of refraction type prism portions to the number ofhybrid type prism portions is gradually increased as the incident angle“a” is decreased. Accordingly, as compared with the Fresnel lens shownin FIG. 12, the transmissivity of the Fresnel lens 14 shown in FIG. 13in the neighborhood of the characteristic changing angle “a0” can besmoothly changed.

In this case, it is preferred that the position of the characteristicchanging angle “a0” in the relationship of the incident angles, thenumber of pitch areas in the characteristic changing region and themixing ratios are determined according to specifications of the Fresnellens 14.

In addition, the transmissivity of a Fresnel lens in the neighborhood ofthe characteristic changing angle “a0” can be smoothly changed accordingto another following improvement.

FIG. 14 is an enlarged view of a sectional shape of another Fresnel lensin a plurality of pitch areas according to the third embodiment of thepresent invention. Each arrow denotes a ray of light.

In FIG. 14, 18 indicates another Fresnel lens according to the thirdembodiment. 19A indicates a hybrid type prism portion of the Fresnellens 18. 19B, 19C and 19D indicate a plurality of hybrid type prismportions (or a plurality of intermediary prism portions) of the Fresnellens 18 respectively. 19E indicates a refraction type prism portion. 3019A-1, 19B-1, 19C-1 and 19D-1 respectively indicate a plurality ofincident planes of a plurality of total reflection type prism portionscomposing the hybrid type prism portions 19A to 19D. 19A-2, 19B-2, 19C-2and 19D-2 respectively indicate a plurality of incident planes of aplurality of refraction type prism portions composing the hybrid typeprism portions 19A to 19D. 19E-2 indicates an incident plane of therefraction type prism portion 19E. 20 indicates an outgoing plane of theFresnel lens 18. The outgoing plane 20 is formed in a flat surfaceshape. m7 indicates a normal of the outgoing plane 20.

Li17 indicates a ray of incident light transmitted to the hybrid typeprism portion 19A at an incident angle “a15” to the normal m7, Li18indicates a ray of incident light transmitted to the hybrid type prismportion 19B at an incident angle “a16” to the normal m7, Li19 indicatesa ray of incident light transmitted to the hybrid type prism portion 19Cat an incident angle “a17” to the normal m7, Li20 indicates a ray ofincident light transmitted to the hybrid type prism portion 19D at anincident angle “a18” to the normal m7, and Li21 indicates a ray ofincident light transmitted to the hybrid type prism portion 19E at anincident angle “a19” to the normal m7.

21B, 21C and 21D respectively indicate hybrid type prism portions basedon the first embodiment corresponding to the incident angles “a16”,“a17” and “a18”. The hybrid type prism portion 21B has a totalreflection plane 21B-1 and an incident plane 21B-2, the hybrid typeprism portion 21C has a total reflection plane 21C-1 and an incidentplane 21C-2, and the hybrid type prism portion 21D has a totalreflection plane 21D-1 and an incident plane 21D-2. Each of the hybridtype prism portions 21B, 21C and 21D is indicated by a dot-dash line tocompare the hybrid type prism portions 21B, 21C and 21D with the hybridtype prism portions 19B, 19C and 19D based on the third embodimentrespectively.

The incident angles satisfy the relationship a15>a16>a17>a18 >a19.Therefore, a most-end portion of the Fresnel lens 18 is placed in anupper direction (or above in FIG. 14) of the hybrid type prism portion19A, and an optical axis of the Fresnel lens 18 is placed in a lowerdirection (or below in FIG. 14) of the refraction type prism portion19E.

The hybrid type prism portion based on the first embodiment is arrangedin each of pitch areas ranging from the most-end portion of the Fresnellens 18 to the hybrid type prism portion 19A, and the refraction typeprism portion based on the prior art is arranged in each of pitch areasranging from the refraction type prism portion 19E to the optical axisof the Fresnel lens 18.

In the Fresnel lens 18 shown in FIG. 14, an area of each of the incidentplanes 19B-1 to 19D-1 placed in pitch areas corresponding to incidentangles (or a characteristic changing region) neighboring to thecharacteristic changing angle “a0” is slightly decreased whilemaintaining a prescribed angle of the incident plane to the ray ofincident light, and the area of each of the incident planes 19B-2 to19D-2 placed in the pitch areas corresponding to the incident anglesneighboring to the characteristic changing angle “a0” is slightlyincreased while maintaining a prescribed angle of the incident plane tothe ray of incident light.

In other words, in FIG. 14, the areas of the incident planes 19B-1 to19D-1 satisfy the relationship of incident plane 19B-1>incident plane19C-1>incident plane 19D-1, and the areas of the incident planes 19B-2to 19D-2 satisfy the relationship of incident plane 19B-2>incident plane19C-2>incident plane 19D-2. As the incident angle is decreased in theorder of “a16”, “a17” and “a18”, the area of the incident plane of thetotal reflection type prism portion of the hybrid type prism portion isslightly decreased in the order of the incident plane 19B-1, theincident plane 19C-1 and the incident plane 19D-1, and the area of theincident plane of the refraction type prism portion of the hybrid typeprism portion is slightly increased in the order of the incident plane19B-2, the incident plane 19C-2 and the incident plane 19D-2.

In short, in cases where the characteristic changing angle “a0” isplaced between the incident angle “a16” and the incident angle “a18”(that is, three pitch areas corresponding to the incident angles “a16”to “a18” denote pitch areas of the characteristic changing region), asthe incident angle is decreased in the order of “a16”, “a17” and “a18”,the areas of the incident planes 19B-1 to 19D-1 are slightly decreasedstep by step in that order, and the areas of the incident planes 19B-2to 19D-2 are slightly increased step by step in that order.

In this case, because the prism portion of the Fresnel lens 18 ischanged step by step from the hybrid type prism portion 19A to therefraction type prism portion 19E through the hybrid type prism portions19B to 19D, the transmissivity of the Fresnel lens 18 in theneighborhood of the characteristic changing angle “a0” can be smoothlychanged. Here, it is preferred that the prescribed angles of theincident planes 19B-1 to 19D-1 and the incident planes 19B-2 to 19D-2 tothe rays of incident light Li18 to Li20 are determined according tospecifications of the Fresnel lens 18.

Also, for example, it is preferred that the incident planes 19B-1 to19D-1 are slightly decreased step by step in parallel to the incidentplanes 21B-2 to 21D-2 of the hybrid type prism portion 21B to 21Drespectively (refer to blank arrows in FIG. 14) to slightly increase theincident planes 19B-2 to 19D-2 by using the incident planes of thehybrid type prism portions 21B to 21D as the incident planes 19B-2 to19D-2.

In this embodiment, the three hybrid type prism portions 19B to 19D areused as the intermediary prism portions. However, the number ofintermediary prism portions (that is, the number of pitch areas of thecharacteristic changing region) is not restricted.

Also, either a degree of the slight decrease of the areas of theincident planes 19B-1 to 19D-1 or a degree of the slight increase of theareas of the incident planes 19B-2 to 19D-2 is not restricted, and it ispreferred that the degree of the slight decrease and the degree of theslight increase are determined so as to improve the transmissivity ofthe Fresnel lens 18.

As is described above, in the third embodiment, the characteristicchanging angle “a0” is used as a boundary, the hybrid type prism portionis arranged in the Fresnel lens 18 for each pitch area corresponding tothe incident angle larger than (or equal to or larger than) thecharacteristic changing angle “a0”, and there fraction type prismportion is arranged in the Fresnel lens 18 for each pitch areacorresponding to the incident angle equal to or smaller than (or smallerthan) the characteristic changing angle “a0”. Accordingly, thetransmissivity of the Fresnel lens 10 in the region of the smallincident angles can be improved.

Also, in the third embodiment, the mixing ratio of the refraction typeprism portions 16C to 16F to the hybrid type prism portions 15C to 15His increased in correspondence to the decrease of the incident angle inthe pitch areas of the characteristic changing region neighboring to thecharacteristic changing angle “a0”. Accordingly, the transmissivity ofthe Fresnel lens 14 in the region of the small incident angles can beimproved, and the transmissivity of the Fresnel lens 14 in theneighborhood of the characteristic changing angle “a0” can be smoothlychanged.

In addition, in the third embodiment, in the neighborhood of thecharacteristic changing angle “a0”, as the incident angle is decreased,the areas of the incident planes 19B-1 to 19D-1 are slightly decreasedin that order, the areas of the incident planes 19B-2 to 19D-2 areslightly increased in that order, and the Fresnel lens 18 comprises thehybrid type prism potions 19B to 19D having the incident planes 19B-1 to19D-1 and the incident planes 19B-2 to 19D-2. Accordingly, thetransmissivity of the Fresnel lens 18 in the region of the smallincident angles can be improved, and the transmissivity of the Fresnellens 18 in the neighborhood of the characteristic changing angle “a0”can be smoothly changed.

Here, it is applicable that the third embodiment be applied to thesecond embodiment.

Embodiment 4

In a fourth embodiment, optimum values of the top blade angle and theoutgoing angle “f” in the hybrid type prism portion 2 described in thefirst embodiment will be described.

Initially, an optimum value of the top blade angle between the incidentplane 4B and the total reflection plane 4C is described.

FIG. 15 is a view showing the transmissivity Tall of the hybrid typeprism portion 2 in case of the top blade angle set to 45 degrees (solidline), the top blade angle set to 40 degrees (two-dot-dash line) and thetop blade angle set to 35 degrees (broken line).

As compared with the case of =45 degrees (the case shown in FIG. 8), inthe region of the large incident angle “a” larger than about 40 degrees,the transmissivity at the top blade angle=40 degrees and thetransmissivity at the top blade angle=35 degrees are the same as that atthe top blade angle=45 degrees and are equal to or higher than 90%.

However, the transmissivity at the top blade angle=45 degrees isdecreased with the decrease of the incident angle “a” in a region of theincident angle “a” equal to or smaller than about 40 degrees. Incontrast, as compared with the case of =45 degrees, it is realized inFIG. 15 that the transmissivity Tall at the top blade angle=40 degreesis high and is equal to or higher than 90% in a range of the incidentangle “a” from 40 degrees to about 35 degrees. Also, in case of the topblade angle=35 degrees, the transmissivity Tall is further high, and ahigh transmissivity region is widened toward the incident angle “a” ofabout 30 degrees.

In short, in the region of the incident angles “a” equal to or smallerthan about 40 degrees, in cases where the top blade angle is set assmall as possible, the dependence of the transmissivity Tall on theincident angle can be reduced, and the high transmissivity of the hybridtype prism portion 2 can be obtained in a wide range of the incidentangle.

Here, as shown in FIG. 15, the top blade angle is set to 40 degrees or35 degrees, the transmissivity is reduced to 60% or less in a region ofthe incident angles “a” equal to or smaller than about 15 degrees.However, in cases where the top blade angle is, for example, set to 45degrees in the hybrid type prism portions 2 corresponding to the regionof the incident angles “a” equal to or smaller than about 15 degrees,the top blade angle set to 45 degrees can prevent the reduction of thetransmissivity.

In detail, at the incident angle “a” equal to about 15 degrees, thetransmissivity for the top blade angle set to 40 degrees is equal to thetransmissivity for the top blade angle set to 45 degrees, and a high andlow relationship between the transmissivity for the top blade angle setto 40 degrees and the transmissivity for the top blade angle set to 45degrees at the incident angle “a” larger than about 15 degrees isinverse to that at the incident angle “a” smaller than about 15 degrees.Therefore, the hybrid type prism portion 2 having the top blade angleset to 40 degrees is arranged in the region of the incident angles “a”ranging from 15 degrees to 90 degrees, and the hybrid type prism portion2 having the top blade angle set to 45 degrees is arranged in the regionof the incident angles “a” ranging from 0 degree to 15 degrees.Accordingly,a transmissivity set by combining the transmissivitycharacteristic (two-dot dash line in FIG. 15) at the top blade angle setto 40 degrees in the region of the incident angles “a” ranging from 15degrees to 90 degrees and the transmissivity characteristic (solid linein FIG. 15) at the top blade angle set to 45 degrees in the region ofthe incident angles “a” ranging from 0 degree to 15 degrees can beobtained.

Also, it is preferred that the reduction of the transmissivity isprevented by using the method described in the third embodiment. In thiscase, a transmissivity set by combining the transmissivitycharacteristic (dot-dash line in FIG. 15) of the refraction type prismportion and the transmissivity characteristic of the hybrid type prismportion at the top blade angle set to 40 degrees is, for example,obtained.

Therefore, in cases where the Fresnel lens 1 based on the firstembodiment is designed, it is preferred that the top blade angle of thehybrid type prism portion 2 is set as acute as possible incorrespondence to the value of the incident angle However, in caseswhere, the top blade angle is excessively set to a small value, an anglebetween the incident plane 4B and the outgoing plane 5 in FIG. 7 ischanged to an obtuse angle in case of a large incident angle “a”, thehybrid type prism portion 2 undesirably has a shape in which it isimpossible to take off a forming mold (or a lens forming mold) from theFresnel lens 1 in the manufacturing of the Fresnel lens 1. Therefore,the top blade angle of the hybrid type prism portion 2 is set to anoptimim value in correspondence to the value of the incident angle whileconsidering the taking-off of the forming mold.

In other words, the top blade angle of the hybrid type prism portion 2is set as acute as possible (or set to an acutest angle) in a range inwhich the acute top blade angle does not adversely influence on themanufacturing of the Fresnel lens 1, and the transmissivity of theFresnel lens 1 can be further improved. Also, in an incident angleregion in which the transmissivity at the top blade angle set to a valueother than that of the acutest angle is higher than the transmissivityat the top blade angle set to the value of the acutest angle, the topblade angle is set to a value larger than that of the acutest angleTherefore, a high transmissivity of the hybrid type prism portion 2 canbe obtained over the entire region of the incident angles.

Next, an optimum value of the outgoing angle “f” of the ray of outgoinglight in the hybrid type prism portion 2 is described.

FIG. 16 is a view showing the transmissivity Tall of the hybrid typeprism portion 2 in case of the outgoing angle “f” set to 0 degree (solidline), the outgoing angle “f” set to 3 degrees (two-dot dash line) andthe outgoing angle “f” set to 5 degrees (broken line).

As shown in FIG. 16, the transmissivity at the outgoing angle “f” set to0 degree, the transmissivity at the outgoing angle “f” set to 3 degreesand the transmissivity at the outgoing angle “f” set to 5 degrees arethe same as each other and are equal to or higher than 90% in the regionof the large incident angles higher than about 40 degrees. In contrast,in the region of the small incident angles equal to or smaller thanabout 40 degrees, the transmissivity at the outgoing angle “f” set to 3degrees is improved as compared with the transmissivity at the outgoingangle “f” set to 0 degree, and the transmissivity at the outgoing angle“f” set to 5 degrees is improved as compared with the transmissivity atthe outgoing angle “f” set to 3 degrees.

Accordingly, the transmissivity Tall of the hybrid type prism portion 2can be improved by enlarging the outgoing angle “f” in the region of thesmall incident angles.

Also, following effects can be obtained by enlarging the outgoing angle“f” in the region of the small incident angles.

FIG. 17A and FIG. 17B are views respectively showing the configurationof an image displaying device in which the Fresnel lens 1 is applied toa screen. FIG. 17A is a constitutional view of the image displayingdevice seen from a side, and FIG. 17B is a front view of the imagedisplaying device. Each arrow denotes a ray of light.

In FIG. 17A, 31 indicates a light emitting source (or illumination lightsource means) for emitting a plurality of rays of light. 32 indicates aparabolic mirror (or illumination light source means). The lightemitting source 31 is disposed on a focal point of the parabolic mirror32. 33 indicates a converging lens (or converging optics means) forconverging a plurality of rays of light reflected on the parabolicmirror 32. 34 indicates a light bulb (or optical modulating means)formed of liquid crystal. An intensity of each ray of light converged bythe converging lens 33 is spatially changed in the light bulb 34 tomodulate the converged rays of light.

35 indicates a projection optics lens (or projection optics means) forforming an image from the rays of light of which the intensities arechanged for the modulation by the light bulb 34. 36 indicates a rearprojection type screen for receiving the image of the rays of lightformed by the projection optics lens 35 from the rear side anddisplaying the image. The rays of light spreading in the projectionoptics lens 35 are changed in the screen 36 to a plurality of rays oflight parallel to each other, the image formed from the rays of light isdisplayed on the screen 36, and the rays of light are diffused from thescreen 36 to a wide area. Therefore, the screen 36 has a function forwidening a view field.

In the screen 36, 37 indicates a Fresnel lens described in eachembodiment, and 38 indicates a lenticular.

In the Fresnel lens 37, the spreading rays of light sent from theprojection optics lens 35 are received according to the function of theFresnel lens 37 described in each embodiment, and the rays of light goout at a prescribed outgoing angle through a plurality of prism portionsof a plurality of pitch areas. In short, the Fresnel lens 37 is used toalmost collimate the rays of light spreading in the projection opticslens 35. An image is formed on the lenticular 38 from the rays of lightgoing out from the Fresnel lens 37, and the rays of light are diffusedfrom the lenticular 38.

39 and 40 respectively indicate an optical axis. The optical axis 39exists for the parabolic mirror 32, the converging lens 33 and the lightbulb 34. The optical axis 40 exists for the projection optics lens 35,the Fresnel lens 37 and the lenticular 38, and the optical axis 40 isperpendicular to the outgoing plane of the Fresnel lens 37.

The optical axis 39 and the optical axis 40 do not intersect each other,and the optical axis 39 and the optical axis 40 are independent of eachother so as to set an angle between the optical axis 39 and the opticalaxis 40 to an optimum setting angle depending on the light bulb 34. Inother words, the parabolic mirror 32, the converging lens 33 and thelight bulb 34 having the same optical axis 39 are arranged so as toshift the center of the parabolic mirror 32, the converging lens 33 andthe light bulb 34 from the optical axis 40.

The image displaying device having an optical system shown in FIG. 17Ahas a front view shown in FIG. 17B. The constituent elements, which arethe same as those shown in FIG. 17A, are indicated by the same referencenumerals as those of the constituent elements shown in FIG. 17A.

In FIG. 17B, 41 indicates a body of the image displaying device. 42indicates a plurality of ring bands of each hybrid type prism portionarranged in the Fresnel lens 37. The ring bands 42 are shown to expressthe relationship of the ring bands 42 to the screen 36. 43 indicates askirt portion of the image displaying device 41. The parabolic mirror32, the converging lens 33 and the light bulb 34 are arranged in theskirt portion 43.

The image displaying device 41 is operated in the same manner as that inthe image displaying device shown in FIG. 2 except that rays of lightare projected from the light bulb 34 having the center shifted from theoptical axis 40 to the screen 36, and the function and operation of theFresnel lens 37 has been already described above. Therefore, thedescription of the operation of the image displaying device 41 isomitted.

Even-numbered image displaying devices 41 respectively having theabove-described structure are prepared, and a group of even-numberedimage displaying devices 41 having a multiple-structure shown in FIG. 18is of ten used.

FIG. 18A, FIG. 18B and FIG. 18C are views explaining a method ofoptimizing the outgoing angle of a ray of outgoing light, and amultiple-structure of two image displaying devices 41 is shown. FIG. 18Ais a sectional shape of a Fresnel lens of which the outgoing angle isoptimized. FIG. 18B is a front view of a screen having the Fresnel lensshown in FIG. 18A. FIG. 18C is a view showing the relationship betweenthe image displaying devices 41 having the multiple-structure and auser.

In FIG. 18A, FIG. 18B and FIG. 18C, 36A and 36B indicate a plurality ofscreens respectively. 37A and 37B indicate a plurality of Fresnel lensesrespectively. 38A and 38B indicate a plurality of lenticularsrespectively. 40A and 40B indicate a plurality of optical axes of theFresnel lenses 37A and 37B respectively. 4A and 41B respectivelyindicate the image displaying device shown in FIG. 17A and FIG. 17B. 42Aindicates a ring band of the Fresnel lens 37A, and 42B indicates a ringband of the Fresnel lense 37B. 43A and 43B indicate a plurality of skirtportions of the image displaying devices 41A and 41B. Each of theFresnel lenses 37A and 37B is formed in a rectangular shape to have foursides, the ring band 42A selected from a plurality of ring bandsintersects only one side closest to the optical axis 40A among the foursides of the Fresnel lens 37A and denotes a boundary ring band, and thering band 42B selected from a plurality of ring bands intersects onlyone side closest to the optical axis 40B among the four sides of theFresnel lens 37B and denotes a boundary ring band. In this case, it isadmitted that the optical axis 40A is not placed on the side of theFresnel lens 37A closest to the optical axis 40A, and it is admittedthat the optical axis 40B is not placed on the side of the Fresnel lens37B closest to the optical axis 40B. The ring bands 42A and 42B aredetermined according to view field characteristics and transmissivity ofthe screens 36A and 36B respectively.

The image displaying device shown in FIG. 18A, FIG. 18B and FIG. 18C isformed to have a multiplex-structure by making the image displayingdevice 41A up-side down to place the skirt portion 43A on the upper sideand connecting the upper side of the screen 36B of the image displayingdevice 41B having the skirt portion 43B on the lower side and the upperside of the screen 36A of the image displaying device 41A. Therefore,one image is divided into two, the two divided images are provided forthe image displaying devices 41A and 41B respectively, the two dividedimages integrally formed with each other are displayed on the imagedisplaying devices 41A and 41B as one image. Accordingly, a furtherlarge-sized image can be displayed.

44 indicates a user of the image displaying devices 41A and 41B. 45indicates an angle of view field. Also, Lo3A to Lo7A denote a pluralityof rays of outgoing light going out from the pitch areas of the Fresnellens 37A respectively, and Lo3B to Lo7B denote a plurality of rays ofoutgoing light going out from the pitch areas of the Fresnel lens 37Brespectively. The rays of outgoing light Lo3A to Lo7A are arranged inthe order of becoming more distant from the optical axis 40A, and therays of outgoing light Lo3B to Lo7B are arranged in the order ofbecoming more distant from the optical axis 40B. As a ray of outgoinglight near to the optical axis 40A or 40B, or a ray of outgoing lightplaced on the inner side (or on the side of the optical axis 40A or 40B)of the ring band 42A or 42B, approaches the optical axis 40A or 40B, theray of outgoing light is designed so as to go out at a larger outgoingangle

As is shown in FIG. 18C, the user 44 views an integrally-formed image ofthe two image displaying devices 41A and 41B having themultiple-structure. In this case, in an image displaying device using anormal Fresnel lens, a plurality of rays of outgoing light going outfrom the Fresnel lens are parallel to the optical axis. Also, thelenticulars 38A and 38B have view field characteristics. Therefore, incases where each ray of outgoing light is viewed in a propagationdirection of a main ray of outgoing light, the ray of outgoing light ismost bright. In contrast, as each ray of outgoing light is viewed in adirection inclined from the propagation direction of the main ray ofoutgoing light, the ray of outgoing light is darkened. Therefore,because an angle of view field for rays of outgoing light near to theskirt portion 43A or 43B is large and because the user 44 views each rayof outgoing light in a direction deeply inclined from the propagationdirection of the main ray of outgoing light going out in a directionnormal to the screen according to the angle of view field, thebrightness of the rays of outgoing light near to the skirt portion 43Aor 43B is usually reduced.

However, in the Fresnel lenses 37A and 37B based on the fourthembodiment, as a pitch area for a ray of outgoing light approaches theoptical axis 40A or 40B, or as an incident angle for a pitch areacorresponding to a ray of outgoing light becomes smaller, the outgoingangle set for the ray of outgoing light becomes larger (a maximumoutgoing angle is set for the rays of outgoing light Lo3A and Lo3B).Therefore, because a main ray of the outgoing light is directed towardthe user 44, a light quantity attenuation based on the view fieldcharacteristics of the lenticulars 38A and 38B can be reduced. Also, thereduction of the light quantity attenuation compensates for thereduction of the transmissivity of the prism portions near to the skirtportions 43A or 43B, and the outgoing angles for the rays of outgoinglight Lo3A to Lo7A and the rays of outgoing light Lo3B to Lo7B can besuitably optimized so as to direct the rays of outgoing light at theangle of view field 45.

As is described above, in cases where the Fresnel lenses 37A and 37B areapplied to the image displaying device having the multiple-structure, abright image can be provided for the user.

Also, as shown in FIG. 19, in cases where a combination of four imagedisplaying devices 41A, 41B, 41C and 41D is used as an image displayingdevice having a multiple-structure, the outgoing angles “f” of aplurality of rays of outgoing light going out from pitch areas placed onthe inner side (or on the side of an optical axis 40A, 40B, 40C or 40D)of a ring band 42A, 42B, 42C or 42D are set to large values in the imagedisplaying devices 41A, 41B, 41C and 41D. In detail, in the same manneras in FIG. 18A to FIG. 18C, the main rays in the rays of outgoing lightgoing out from pitch areas placed on the inner side of the ring band42A, 42B, 42C or 42D are directed toward the user 44A. Also, the rays ofoutgoing light going out from pitch areas placed on the outer side ofthe ring band 42A, 42B, 42C or 42D are set to be parallel to the opticalaxis 40A, 40B, 40C or 40D. In the same manner as the case in FIG. 18A toFIG. 18C, each of the ring bands 42A, 42B, 42C and 42D selected from aplurality of ring bands intersects only one side closest to the opticalaxis 40A, 40B, 40C or 40D among four sides of a rectangular-shapedFresnel lens composing the screen 36A, 36B, 36C or 36D and denotes aboundary ring band. The ring bands 42A, 42B, 42C and 42D are determinedaccording to view field characteristics and transmissivity of thescreens 36A, 36B, 36C and 36D respectively.

In the neighborhood of boundaries among the screens 36A, 36B, 36C and36D of the image displaying devices 41A, 41B, 41C and 41D integrallyformed with each other, it is required to make main rays in the rays ofoutgoing light be parallel to the optical axis 40A, 40B, 40C or 40D. Indetail, in cases where a user 44B views the screens 36A, 36B, 36C and36D on a slant, the user 44B views boundary areas of each pair ofscreens adjacent to each other through a boundary on a slant at acertain angle of view field, and the brightness of images displayed onthe boundary areas is reduced due to the light quantity attenuationbased on the view field characteristics of the screens. However, becausea degree of the light quantity attenuation in the boundary area of onescreen is the same as that in the boundary area of the other screen, theunevenness of luminance in the boundary areas of each pair of screensadjacent to each other can be prevented, and the user 44B can viewimages of the screens having the uniform luminance. In addition, becausethe outgoing angles “f” of the rays of outgoing light going out frompitch areas placed on the inner side of the ring band 42A, 42B, 42C or42D are set to large values, the luminance of the image lowered on theinner side of the ring band 42A, 42B, 42C or 42D can be improved, andthe uniformity of the luminance of the image displayed on the screens36A, 36B, 36C and 36D can be improved.

As is described above, a Fresnel lens is cut out in a rectangular shapein correspondence to a shape of each screen, a ring band intersectingonly one side closest to the optical axis of each Fresnel lens amongfour sides of the Fresnel lens is set as a boundary ring band, aplurality of rays of outgoing light going out from a plurality of pitchareas placed on the optical axis side of each boundary ring band are setto large values, and a plurality of rays of outgoing light going outfrom a plurality of pitch areas placed on the lens outer-curcumferentialside of each boundary ring band are set to be parallel to the opticalaxis of the Fresnel lens. Accordingly, in cases where a plurality ofFresnel lenses are applied to the screens of the image displaying devicehaving a multiple-structure, the uniformity of the luminance of theimage displayed on the screens can be improved.

As is apparent in FIG. 17A, FIG. 17B, FIG. 18A, FIG. 18B, FIG. 18C, andFIG. 19, it is preferred that a screen comprises the Fresnel lensdescribed in each embodiment and an image forming and diffusing meanssuch as a lenticular used to form an image from light and to diffuse theimage. In this case, because projected rays of light at a wide imageangle can be received on the screen at a high transmissivity whilehardly depending on the incident angle, a screen displaying alarge-sized image at a high transmissivity on condition of aspecification of a predetermined thickness can be obtained.

Also, in cases where the Fresnel lens described in each embodiment isapplied to the screen, it is preferred that the lenticular is integrallyformed with the outgoing plane of the Fresnel lens. In this case, ascreen having a reduced number of constituent parts can be obtained.

Embodiment 5

FIG. 20 is a view of the whole structure of a rear projection type imagedisplaying device according to a fifth embodiment of the presentinvention.

An image displaying device shown in FIG. 20 comprises a screen 53 and animage light source 54. The screen 53 comprises a Fresnel lens 51 and adiffusion plate 52. Rays of image light are injected from the imagelight source 54 to display an image on the screen 53. An aspect ratio inthe screen 53 is set to 4:3, and a size of the screen 53 is set to 50inches.

FIG. 21 is a view of the image displaying device shown in FIG. 20 seenfrom one side. The screen 53 is arranged so as to set a distance betweenthe screen 53 and the image light source 54 in a horizontal direction to450 mm and so as to set a distance between a bottom end of the screen 53and the image light source 54 in a perpendicular direct ion to 200 mm.

The diffusion plate 52 has a lenticular lens and functions as a lightdiffusing means for diffusing the rays of image light to a prescribedarea.

The Fresnel lens 51 is obtained by arranging a plurality of smallunit-prism portions and is formed of a circular type Fresnel lens inwhich a plurality of unit-prism portions are concentrically arranged.The image light source 54 is disposed on a line which is perpendicularto the Fresnel lens 51 and extends from the center of concentric circlesof the Fresnel lens 51, and a portion of an area specified by theconcentric circles shifting from the center (called a Fresnel center) ofthe Fresnel lens 51 is used as the Fresnel lens 51 (refer to FIG. 20).

FIG. 22 is a view showing a sectional shape of the Fresnel lens 51.

The Fresnel lens 51 can be partitioned into three regions A1, A2 and A3in a direction from the Fresnel center side to the periphery (called aFresnel periphery) side of the Fresnel lens 51.

As a basic shape of the Fresnel lens 51, the Fresnel lens 51 of theregion A2 will be initially described.

Each unit-prism portion (or a hybrid type prism portion) in the regionA2 has a total reflection type prism portion U1 and a refraction typeprism portion U2. The total reflection type prism portion U1 has anincident plane (or a second incident plane) 5IA and a total reflectionplane 51B, and a vertex angle between the planes are set to 40 degrees.The refraction type prism portion U2 has an incident plane (or a firstincident plane) 51C and an ineffective plane 51D. The unit-prism portionranges from a first trough line T to a second trough line T adjacent tothe first trough line, and each trough line T is defined as a line onwhich the ineffective plane 51D of a first unit-prism portion intersectsthe total reflection plane 51B of a second unit -prism portion adjacentto the first unit-prism portion. A pitch of each unit-prism portion inthe region A2 is set to 0.1 mm. Also, a pitch of each unit-prism portionin the region Al and a pitch of each unit-prism portion in the region A3are set to the same length as that in the region A2.

FIG. 23A, FIG. 23B and FIG. 23C are views explaining the totalreflection type prism portion U1 and the refraction type prism portionU2.

FIG. 23A shows a Fresnel lens (or a conventional Fresnel lens havingonly a plurality of refraction type prism portions) formed of aplurality of unit-prism portions respectively having a shape equivalentto the refraction type prism portion U2. As is described above, a fluxof light R1 in projected on the incident plane 51C is refracted on theincident plane 51C and goes out in a desired direction. However, a fluxof light R2 in projected on the ineffective plane 51D is reflected orrefracted on the ineffective plane 51D and is undesirably changed tostray light.

FIG. 23B shows a Fresnel lens (or a conventional Fresnel lens havingonly a plurality of the total reflection type prism portions) formed ofa plurality of unit-prism portions respectively having a shapeequivalent to the total reflection type prism portion U1. As isdescribed above, a partial flux of light R3 in among a flux of lightprojected on the incident plane 51A is totally reflected on the totalreflection plane 51B and goes out in a desired direction. However, theremaining flux of light R4 in projected on the incident plane 51A cannotreach the total reflection plane 51B and is undesirably changed to straylight.

FIG. 23C shows a Fresnel lens 51 according to the fifth embodiment. Inthe Fresnel lens 51, a unit-prism portion is formed by combining onetotal reflection type prism portion U1 and one refraction type prismportion U2, and a flux of light impossible to go out in the desireddirection in the Fresnel lens of FIG. 23A composed of only therefraction type prism portions U2 or a flux of light impossible to goout in the desired direction in the Fresnel lens of FIG. 23B composed ofonly the total reflection type prism portions U1 can go out in thedesired direction (or a direction almost perpendicular to the outgoingplane of the Fresnel lens 51) in the Fresnel lens 51.

In detail, in the Fresnel lens 51, the refraction type prism portions U2is arranged on a part of an optical path through which the flux of lightR4 in not reaching the total reflection plane 51B of the totalreflection type prism portions U1 is projected on the incident plane 51Ain the Fresnel lens of FIG. 23B. Therefore, in the Fresnel lens 51, apart of the flux of light R4 in is refracted to deflect the part of theflux of light R4 in and goes out in the desired direction.

This arrangement of the total reflection type prism portions U1 and therefraction type prism portions U2 in the Fresnel lens 51 can be viewedfrom another angle That is to say, on a part of an optical path of theflux of light R2 in projected on the ineffective plane 51D of therefraction type prism portion U2 of a first pitch area (or a firstunit-prism portion), the total reflection type prism portion U1 of asecond pitch area (or a second unit-prism portion) adjacent to the firstpitch area on the Fresnel center side is arranged. Therefore, in theFresnel lens 51, a part of the flux of light R2 in is totally reflectedto deflect the part of the flux of light R2 in and goes out in thedesired direction. In other words, the refraction type prism portion U2of the Fresnel lens 51 shown in FIG. 23C is arranged so as to compensatefor demerits of the total reflection type prism portions U1 of theFresnel lens shown in FIG. 23B, and the total reflection type prismportion U1 of the Fresnel lens 51 shown in FIG. 23C is arranged so as tocompensate for demerits of the refraction type prism portions U2 of theFresnel lens shown in FIG. 23A.

Also, in each pitch area (or unit-prism portion) of the region A2 shownin FIG. 22, as shown in FIG. 23C, the total reflection type prismportion U1 and the refraction type prism portion U2 are arranged so asto make an extending plane of the incident plane 51C intersect thetrough line T placed on the Fresnel periphery side of the incident plane51C and so as to make an extending plane of the incident plane 51Aintersect the trough line T placed on the Fresnel center side of theincident plane 51A. The reason of the arrangement of the totalreflection type prism portions U1 and the refraction type prism portionsU2 in the region A2 is based on a manufacturing method of the Fresnellens 51. Next, a method of manufacturing the Fresnel lens 51 will bedescribed below.

The Fresnel lens 51 is manufactured by forming resin in a specificshape. Therefore, it is required to manufacture a lens forming moldwhich is formed in a shape obtained by reversing a shape of the Fresnellens 51.

FIG. 24A, FIG. 24B, FIG. 24C, FIG. 25A, FIG. 25B and FIG. 25C are viewsexplaining features of a lens forming mold used for the manufacturing ofthe Fresnel lens 51. FIG. 24A to FIG. 24C show manufacturing steps ofcutting a portion corresponding to the total reflection type prismportions U1, and FIG. 25A to FIG. 25C show manufacturing steps ofcutting a portion corresponding to the refraction type prism portionsU2.

In FIG. 24A to FIG. 24C and FIG. 25A to FIG. 25C, a symbol C indicates alens forming mold, and a symbol B indicates a cutting tool (or a bite)such as a diamond bite for cutting the lens forming mold C.

The lens forming mold C is manufactured according to the cutting workusing the cutting tool B. In this case, to prevent scratches orirregularity from being generated on the surface of the lens formingmold C, a pointed end (or a corner) of the cutting tool B (or a chip) isnot used, but it is required to cut the lens forming mold C by using acutting blade (or an inclined plane portion) of he cutting tool B. Also,though the pitch of a Fresnel lens is equal to almost 0.1 mm (0.1 mm incase of the Fresnel lens 51), a size of the chip of the cutting tool Branges 10 from 2 to 3 mm.

Therefore, unless a following cutting condition (A) or (B) is satisfied,a lens forming mold corresponding to the shape of the unit-prism portioncannot be manufactured according to the cutting work.

Cutting Condition (A)

A plane obtained by extending the incident plane 51C intersects thetrough line T (refer to FIG. 25B) or passes through a position shiftedfrom the trough line T toward the light outgoing side (refer to FIG.25C).

Cutting Condition (B)

A plane obtained by extending the incident plane 51A intersects thetrough line T (refer to FIG. 24B) or passes through a position shiftedfrom the trough line T toward the light outgoing side (refer to FIG.24C).

To manufacture the Fresnel lens 51 based on the fifth embodiment, thecutting tool B (or a chip) having a vertex angle of 40 degrees is used,and the cutting work is performed for a portion of the lens forming moldC corresponding to the total reflection type prism portion U1 and therefraction type prism portion U2.

<Manufacturing of Lens Forming Mold>

FIG. 26 is a flow chart showing a method of manufacturing a lens formingmold according to the fifth embodiment of the present invention. Also,FIG. 27A, FIG. 27B, FIG. 27C and FIG. 27D show steps of a cutting workfor the manufacturing of the lens forming mold C using the cutting toolB, and FIG. 28A, FIG. 28B, FIG. 28C and FIG. 28D show steps of anothercutting work for the manufacturing of the lens forming mold C using thecutting tool B. FIG. 27A to FIG. 27D correspond to a Fresnel lens inwhich the refraction type prism portion U2 is regarded as a mainunit-prism portion, and FIG. 28A to FIG. 28D correspond to a Fresnellens in which the total reflection type prism portion U1 is regarded asa main unit-prism portion.

In FIG. 26, a pitch number n=1 is set in a step ST1 (or a cutting startpitch number setting step). When the procedure proceeds from the stepST1 to a step ST2 (or a main unit-prism portion cutting step), a cuttingwork for a main unit-prism portion placed in the first pitch area (or acutting pitch area) P1 is performed by using the cutting tool B. Thiscutting work is shown in FIG. 27A or FIG. 28A, the lens forming mold Cis cut in a reversed shape (or a forming mold) of the main unit-prismportion by using the cutting tool B.

When the cutting of the lens forming mold C in the reversed shape of themain unit-prism portion of the first pitch area P11 is completed in thestep ST2, the procedure proceeds to a step ST3 (or a subsidiaryunit-prism portion cutting step), a cutting work for a portion of thelens forming mold C corresponding to a subsidiary unit-prism portionplaced in the first pitch area (or the cutting pitch area) P1 isperformed. As is described with reference to FIG. 25A to FIG. 25C andFIG. 26A to FIG. 26C, in cases where the lens forming mold C is cut in areversed shape (or a forming mold) of the subsidiary unit-prism portionby using the cutting tool B, the cutting work is performed whilesatisfying the cutting condition (A) or the cutting condition (B). Thiscutting work is shown in FIG. 27B or FIG. 28B.

For example, as shown in FIG. 27B, in cases where the lens forming moldC, in which a reversed shape of the refraction type prism portion placedin the first pitch has been already formed as a main unit-prism portion,is cut in a reversed shape of the total reflection type prism portionplaced in the first pitch area P1, the lens forming mold C is cutaccording to the cutting condition (B) so as to make an extending planeSA1 of the incident plane 51A intersect the trough line T1 placed on theFresnel center side of the first pitch area P1 or pass through aposition shifted from the trough line T1 of the Fresnel center sidetoward the light outgoing side.

In the same manner, as shown in FIG. 28B, in cases where the lensforming mold C, in which a reversed shape of the total reflection typeprism portion placed in the first pitch has been already formed as amain unit-prism portion, is cut in a reversed shape of the refractiontype prism portion placed in the first pitch area P1, the lens formingmold C is cut according to the cutting condition (A) so as to make anextending plane SC1 of the incident plane 51C intersect the trough lineT0 placed on the Fresnel periphery side of the first pitch area P1 orpass through a position shifted from the trough line T0 placed on theFresnel periphery side toward the light outgoing side.

When the cutting work for the first pitch area P1 in the Step ST2 andthe step ST3 is completed, the procedure proceeds to a step ST4 (or apitch number incrementing step), the pitch number “n” is incremented to2 (n=2). In a next step ST5 (or a cutting completion judging step), thepitch number “n” is compared with a total number N of pitch areas of thelens forming mold C. In case of n Nmax, or in cases where a pitch areato be cut remains (“NO” in the step ST5), the procedure returns to thestep ST2, and the cutting work (FIG. 27C or FIG. 28C) for a portion ofthe lens forming mold C corresponding to the main unit-prism portionplaced in the second pitch area (or a cutting pitch area) P2 isperformed.

Thereafter, in the step ST3, the cutting work (FIG. 27D or FIG. 28D) fora portion of the lens forming mold C corresponding to the subsidiaryunit-prism portion placed in the second pitch area (or the cutting pitcharea) P2 is performed. In this case, in the same manner as in the firstpitch area P1, the cutting work for the second pitch area P2 isperformed in the step ST3 so as to satisfy the cutting condition

(A) or the Cutting Condition (B).

For example, in case of the cutting work shown in FIG. 27D, in caseswhere the lens forming mold C, in which a reversed shape of therefraction type prism portion placed in the second pitch area P2 hasbeen already formed as a main unit-prism portion, is cut in a reversedshape of the total reflection type prism portion placed in the secondpitch area P2, the lens forming mold C is cut according to the cuttingcondition (B) so as to make an extending plane SA2 of the incident plane51A intersect the trough line T2 placed on the Fresnel center side ofthe second pitch area P2 or pass through a position shifted from thetrough line T2 of the Fresnel center side toward the light outgoingside.

In the same manner, in case of the cutting work shown in FIG. 28D, incases where the lens forming mold C, in which a reversed shape of thetotal reflection type prism portion placed in the second pitch area P2has been already formed as a main unit-prism portion, is cut in areversed shape of the refraction type prism portion placed in the secondpitch area P2, the lens forming mold C is cut according to the cuttingcondition (A) so as to make an extending plane SC2 of the incident plane51C intersect the trough line T1 placed on the Fresnel periphery side ofthe second pitch area P2 or pass through a position shifted from thetrough line T1 placed on the Fresnel periphery side toward the lightoutgoing side.

Thereafter, the pitch number “n” is incremented each time the step ST4is performed, and the cutting work is repeatedly performed until thepitch number “n” reaches Nmax (n=Nmax). When n=Nmax+1 is obtained in thestep ST4, the complement of the cutting work for the lens forming mold Cof the Fresnel lens 51 is judged in the step ST5, the manufacturing ofthe lens forming mold cis completed. As is described above, in the fifthembodiment, the manufacturing of the lens forming mold C can be easilyperformed by using a normal cutting tool. Also, because the portioncorresponding to the main unit-prism portion and the portioncorresponding to the subsidiary unit-prism portion are respectively cutfor each pitch area, the precision of the manufacturing of the lensforming mold C can be improved. Therefore, the Fresnel lens 51 can bemanufactured with high precision, and an optical performance of theFresnel lens 51 expected in the designing of the Fresnel lens 51 can beobtained.

In the fifth embodiment, as shown in FIG. 27A to FIG. 27D and FIG. 28Ato FIG. 28D, the cutting work is performed in the direction from theFresnel center side to the Fresnel periphery side. However, the cuttingdirection is not restricted, and it is applicable that the cutting workbe performed in the direction from the Fresnel periphery side to theFresnel center side.

Thereafter, resin is poured into the lens forming mold C manufactured inthe above-described method, the resin is hardened, the lens forming moldC is taken off from the hardened resin, and the manufacturing of theFresnel lens 51 is completed. This Fresnel lens 51 is formed in a shapeof a large-sized lens sheet of 50 inches. Also, because rays of imagelight are projected on the Fresnel lens 51 in an oblique direction, adifference between incident angles of rays of image light depends onincident positions of the rays of image light. In cases where theincident angles of rays of image light incident on the total reflectiontype prism portion U1 are large, an amount of fluxes of light going outin a desired direction is increased. In contrast, in cases where theincident angles of rays of image light incident on the refraction typeprism portion U2 are large, an amount of fluxes of light going out in adesired direction is increased. Accordingly, the total reflection typeprism portion U1 is appropriate to the incident position correspondingto the large incident angle, and the refraction type prism portion U2 isappropriate to the incident position corresponding to the small incidentangle

Therefore, as shown in FIG. 22, in the region A1 (or the Fresnel centerside) nearest to the image light source 54 in the Fresnel lens 51 basedon the fifth embodiment, each refraction type prism portion U2 is set asa main unit-prism portion, and each total reflection type prism portionU1 is set as a subsidiary unit-prism portion, and a ratio of an areaoccupied by the total reflection type prism portion U1 to one pitch areais set to be smaller than a ratio of an area occupied by the refractiontype prism portion U2 to one pitch area.

In contrast, in the region A3 (or the Fresnel periphery side) farthestfrom the image light source 54, each total reflection type prism portionU1 is set as a main unit-prism portion, and each refraction type prismportion U2 is set as a subsidiary unit-prism portion, and a ratio of anarea occupied by the refraction type prism portion U2 to one pitch areais set to be smaller than a ratio of an area occupied by the totalreflection type prism portion U1 to one pitch area.

Here, to change an are a ratio of the total reflection type prismportions U1 to the refraction type prism portions U2, a cutting depth ofthe cutting tool B used to cut the lens forming mold C is changed withthe incident position, and the height of the total reflection type prismportion U1 and the height of the refraction type prism portion U2 arechanged.

FIG. 29 is a view showing the relationship among a radius of the Fresnellens 51 measured from the Fresnel center, a ratio of an area occupied bythe total reflection type prism portion U1 and a ratio of an areaoccupied by the refraction type prism portion U2 to the area of theFresnel lens 51. In FIG. 29, a line L1 and a line L2 are additionallyshown, the line L1 indicates the transmissivity in the pitch areaincluding only the total reflection type prism portion U1, and the lineL2 indicates the transmissivity in the pitch area including only therefraction type prism portion U2. Here, the transmissivity is measuredfor the Fresnel lens 51 arranged in the same manner as in the rearprojection type image displaying device of the fifth embodiment, and awhite light source is used. In FIG. 29, an X-axis indicates a radius inmillimeter, a Y-axis on the left side indicates the transmissivity inpercent (%), and a Y-axis on the right side indicates a lens ratio.

In FIG. 29, the line L1 and the line L2 intersect each other at aposition corresponding to the radius of 250 mm, the effect (or thetransmissivity) of the refraction type prism portion U2 is higher thanthat of the total reflection type prism portion U1 at a region smallerthan the radius of 250 mm (Li<L2), and the effect (or thetransmissivity) of the total reflection type prism portion U1 is higherthan that of the refraction type prism portion U2 at a region largerthan the radius of 250 mm (Li>L2). In the Fresnel lens 51, a ratio of anarea occupied by the total reflection type prism portion U1 to one pitcharea and a ratio of an area occupied by the refraction type prismportion U2 to one pitch area are respectively changed by setting astandard of the ratio at the radius of 250 mm.

In FIG. 29, the height of the total reflection type prism portion U1 orthe refraction type prism portion U2 at the region A2 is set to unity,and a ratio of an area occupied by the total reflection type prismportion U1 to one pitch area or a ratio of an area occupied by therefraction type prism portion U2 to one pitch area is indicated by aratio of the height of the total reflection type prism portion U1 or therefraction type prism portion U2 at an arbitrary position to unity setfor the region A2. The ratio is called a lens ratio. In FIG. 29, a lensratio for the total reflection type prism portion U1 is indicated by aline L3, and a lens ratio for the refraction type prism portion U2 isindicated by a line L4. Here, the area ranging from the radius of 200 mmto the radius of 1078 mm are used as the Fresnel lens 51. However, inFIG. 29, the lines L1 to L4 are indicated in a region ranging from theradius of 100 mm to the radius of 500 mm because the difference betweenthe lines L1 and L2 and the difference between the lines L3 and LA areclearly indicated in the region.

As is realized with reference to FIG. 29, the total reflection typeprism portion U1 does not exist in a region smaller than the radius of200 mm, the increase of a ratio of an area occupied by the totalreflection type prism portion U1 to one pitch area is started at theradius of 200 mm, the lens ratio for the total reflection type prismportion U1 reaches unity (which is equal to the ratio at the region A2)at the radius of 250 mm, and the lens ratio for the total reflectiontype prism portion U1 is kept to unity in a region larger than theradius of 250 mm.

In contrast, the lens ratio for the refraction type prism portion U2 isequal to unity (which is equal to the ratio for the region A2) in aregion smaller than the radius of 300 mm, and the lens ratio for therefraction type prism portion U2 is gradually decreased in a regionequal to or larger than the radius of 300 mm.

Because a ratio of an area occupied by the total reflection type prismportion U1 to one pitch area and a ratio of an area occupied by therefraction type prism portion U2 to one pitch area are respectivelychanged in the Fresnel lens 51, a region smaller than the radius of 250mm is set as the region A1, a region ranging from the radius of 250 mmto the radius of 300 mm is set as the region A2, and a region largerthan the radius of 300 mm is set as the region A3.

Here, it is applicable that the lens ratio for the refraction type prismportion U2 be gradually decreased in a region larger than the radius of250 mm to omit the region A2 from the Fresnel lens 51. However, in thefifth embodiment, the pitch areas of the region A2 are arranged in theFresnel lens 51 to smoothly change the lens ratio and to lessen aluminance difference in an image displayed on the screen.

<Comparison of Transmission>

The Fresnel lens 51 based on the fifth embodiment is manufactured, andit is ascertained that the transmissivity of the Fresnel lens 51 isimproved as compared with that in the prior art.

Here, to compare the Fresnel lens 51 based on the fifth embodiment witha Fresnel lens 110 based on the prior art shown in FIG. 6 according tothe method disclosed in Published Unexamined Japanese Patent ApplicationNo. S61-52601 of 1986, specifications other than shape in the Fresnellens 51 are set to be the same as those in the Fresnel lens 110, and theFresnel lens 51 is manufactured.

FIG. 30 is a view showing the configuration of the Fresnel lens 110according to the prior art. A basic shape of a total reflection typeprism portion and a basic shape of a refraction type prism portion inthe Fresnel lens 110 are set to the same as those in the Fresnel lens51, and the pitch P in the Fresnel lens 110 is set to 0.1 mm which isthe same as that in the Fresnel lens 51.

FIG. 31 is a view showing a lens ratio for a total reflection type prismportion in the Fresnel lens 110 shown in FIG. 30, and the lens ratio isindicated by a line L5. In the Fresnel lens 110, a total reflection typeprism portion U1 and a refraction type prism portion U2 are arrangedindependent of each other, and a lens ratio for the total reflectiontype prism portion U1 and a lens ratio for the refraction type prismportion U2 are shown in an out-of-graph area on a right side in FIG. 31.Here, the lines L1 and L2 in FIG. 31 are the same as those in FIG. 29.

FIG. 32 is a view showing the transmissivity of the Fresnel lens 51based on the fifth embodiment and the transmissivity of the Fresnel lens110 based on the prior art. In FIG. 32, the transmissivity of theFresnel lens 51 is indicated by a line L6, and the transmissivity of theFresnel lens 110 is indicated by a line L7. Also, the lines L1 and L2are shown in the same manner as in FIG. 29 and FIG. 31. Thetransmissivity indicated by the line L6 is high in the whole region ascompared with those indicated by the lines L1, L2 and L7. Therefore, theinventors ascertain that the transmissivity of the Fresnel lens 51 ishigh.

As is described above, in the fifth embodiment, a ratio of an areaoccupied by the total reflection type prism portion U1 to one pitch areaand a ratio of an area occupied by the refraction type prism portion U2to one pitch area are respectively changed, and the total reflectiontype prism portion U1 and the refraction type prism portion U2 arecombined as a unit-prism portion. Therefore, the total reflection typeprism portion U1 of the unit-prism portion can compensate for demeritsof the refraction type prism portion U2, and the refraction type prismportion U2 of the unit-prism portion can compensate for demerits of thetotal reflection type prism portion U1. Accordingly, the Fresnel lens 51having the high transmissivity in the whole region including the regionsA1 to A3 can be obtained.

Also, in the fifth embodiment, because the cutting work for themanufacturing of the lens forming mold C can be performed by using onlyone cutting tool, the Fresnel lens 51 can be easily manufactured.

Accordingly, the screen 53 using the Fresnel lens 51 has hightransmissivity as a whole, an image displayed on the rear projectiontype image displaying device can be made bright, and the rear projectiontype projected image displaying device can be obtained at low cost.

The fifth embodiment is not restricted to the above-described Fresnellens 51, and various modifications and changes can be allowed for theFresnel lens 51.

<First Modification>

In the above-described Fresnel lens 51, the Fresnel lens 51 having thethree regions A1, A2 and A3 is described as an example. However, thefifth embodiment is not restricted to the Fresnel lens 51 having thethree regions A1, A2 and A3, and it is applicable that the combinationof the three regions A1, A2 and A3 be appropriately changed. Forexample, it is applicable that the Fresnel lens 51 have only both theregion A1 and the region A2, or it is applicable that the Fresnel lens51 have only the region A1, the region A2 or the region A3.

<Second Modification>

In the above-described Fresnel lens 51, the outgoing plane of theFresnel lens 51 is flat. However, the fifth embodiment is not restrictedto the Fresnel lens 51 having the flat outgoing plane. For example, itis applicable that an element having a fresnel lens shape be added tothe Fresnel lens 51, or it is applicable that a diffusing means such asa very small irregularity element be added to the Fresnel lens 51.

<Third Modification>

In the above-described Fresnel lens 51, rays of image light emitted fromthe image light source 54 are directly injected on to the Fresnel lens51. However, the fifth embodiment is not restricted to this Fresnel lens51. For example, it is applicable that an optical means such as a mirroror a prism be arranged to change the optical path of rays of image lightemitted from the image light source 54 by the reflection or refractionand to project the rays of image light on to the Fresnel lens 51.

Embodiment 6

In cases where the lens forming mold is manufactured according to themethod of manufacturing the lens forming mold, distortion occurs in thelens forming mold due to malleability of metal. Because the distortionof the lens forming mold causes distortion of an optical plane of aFresnel lens, the optical performance of the Fresnel lens is degradeddue to the distortion of the optical plane of the Fresnel lens.

In the sixth embodiment, the occurrence of distortion in the lensforming mold is initially described, and a method of manufacturing thelens forming mold is described on condition that the method preventsdistortion from occurring in the lens forming mold and guarantees theoptical performance of the Fresnel lens. Also, a method of manufacturingthe lens forming mold is described on condition that an excellentoptical performance is obtained in a Fresnel lens, in which theintermediary prism portions corresponding to incident angles neighboringto the characteristic changing angle described in the third embodimentare used, even though the distortion of the lens forming mold influenceson the Fresnel lens.

FIG. 33A to FIG. 33F are views explaining distortion occurring in aplurality of manufacturing steps of the lens forming mold, and themanufacturing steps are based on the method of manufacturing the lensforming mold described in the fifth embodiment. The constituentelements, which are the same as those shown in FIG. 28, are indicated bythe same reference numerals as those of the constituent elements shownin FIG. 28. The cutting work is performed in the manufacturing stepsshown in FIG. 33A to FIG. 33F in the direction from the Fresnel centerto the Fresnel periphery for each pitch area. After a forming mold (or areversed shape) of the total reflection type prism portion functioningas a main unit-prism portion is produced in the cutting work, a formingmold (or a reversed shape) of the refraction type prism portionfunctioning as a subsidiary unit-prism portion is produced in thecutting work.

Initially, the lens forming mold is cut with the cutting tool B to formaforming mold of a total reflection type prism portion (hereinafter,called a total reflection type prism portion forming mold) correspondingto the first pitch area P1 (FIG. 33A). Thereafter, the lens forming moldis cut with the cutting tool B to form a forming mold of a refractiontype prism portion (here in after, called are fraction type prismportion forming mold) corresponding to the first pitch area P1 (FIG.33B). Therefore, the production of a forming mold of a hybrid type prismportion (hereinafter, called a hybrid type prism portion forming mold)corresponding to the first pitch area P1 is completed. In this case, thecutting conditions are the same as those described in the fifthembodiment.

Next, the procedure proceeds to the cutting work for the second pitcharea P2. A total reflection type prism portion forming moldcorresponding to the second pitch area P2 is formed by the cutting workand is shown in FIG. 33C. In this case, a sharp tip portion placed onthe trough line T1 is generated between the total reflection plane ofthe total reflection type prism portion forming mold corresponding tothe first pitch area P1 and the incident plane of the total reflectiontype prism portion forming mold corresponding to the second pitch areaP2.

Thereafter, as shown in FIG. 33D, the cutting tool B is attached to andpushed toward the tip portion placed on the trough line T1, and the lensforming mold C is cut to form the refraction type prism portion formingmold corresponding to the second pitch area P2. The distortion of thelens forming mold C described in the opening paragraph of this sixthembodiment occurs when the lens forming mold C is cut to form therefraction type prism portion forming mold corresponding to the secondpitch area P2.

In detail, because the width of the tip portion placed on the troughline T1 is narrowed toward the vertex of the tip portion, the strengthof the tip portion on the trough line T1 is weakened toward the vertexof the tip portion. Therefore, as shown in FIG. 33E, when the cuttingtool B is attached to and pushed toward the sharp tip portion placed onthe trough line T1, a pushing force generated in the direction from thesecond pitch area P2 to the first pitch area P1 becomes larger as aposition of the tip portion on the trough line T1 pushed by the cuttingtool B approaches the vertex of the tip portion placed on the troughline T1, and the distortion of the lens forming mold C occurs due tomalleability of metal within an area indicated by a dotted circle NG ofFIG. 33E.

FIG. 33F is an enlarged view of the tip portion on the trough line T1placed within the dotted circle NG of FIG. 33E.

In FIG. 33F, the pushing force of the cutting tool B in the directionfrom the second pitch area P2 to the first pitch area P1 becomesstronger as the tip portion on the trough line T1 pushed by the cuttingtool B approaches the vertex of the tip portion placed on the troughline T1. Therefore, distortion occurs in the total reflection planehaving a cut shape in the first pitch area P1. For example, in caseswhere a cut shape of the total reflection plane according to the designis indicated by a two-dot dash line Real, distortion of the lens formingmold C is indicated by a dot-dash curved line Err.

In the same manner, the same cutting work is repeated for the thirdpitch are a P3 and pitch are as following the third pitch area P3.Therefore, when the lens forming mold C is cut to form a refraction typeprism portion forming mold of the (n+1)-th pitch area Pn+1 (n is anatural number), distortion undesirably occurs in the tip portion on atrough line Tn placed between then-th pitch area Pn already cut and the(n+1)-th pitch area Pn+1 currently cut. In the Fresnel lens manufacturedfrom the lens forming mold C as is described above, the shape of eachtotal reflection plane is deformed to a certain degree corresponding toa degree of the distortion occurring in the tip portion placed on thecorresponding trough line, and the optical performance is degraded.Therefore, for example, loss of rays of light is increased. In caseswhere the degrees of distortion in the pitch areas are distributed inrandom, the rays of outgoing light are unnaturally and discontinuouslydistributed in strength.

By considering the occurrence of the distortion in the lens forming moldC, the method of manufacturing the lens forming mold is improved asfollows.

FIG. 34 is a flow chart showing a method of manufacturing a lens formingmold according to the sixth embodiment of the present invention. Thesteps, which are the same as those shown in FIG. 26, are indicated bythe same symbols as those of the steps shown in FIG. 26. Also, FIG. 35Ato FIG. 35F are views showing the shape of the lens forming mold C cutstep by step according to the method of manufacturing a lens formingmold shown in FIG. 34. The constituent elements, which are the same asthose shown in FIG. 28 or one of FIG. 33A to FIG. 33F, are indicated bythe same reference numerals as those of the constituent elements shownin FIG. 28 or one of FIG. 33A to FIG. 33F. In the same manner as in FIG.33A to FIG. 33F, the cutting work is performed from the Fresnel centerto the Fresnel periphery in the order of a total reflection type prismportion forming mold and a refraction type prism portion forming mold.

In FIG. 34, in the same manner as in the fifth embodiment, a pitchnumber n=1 is set in a step ST1 (or a cutting start pitch number settingstep). In a step ST2 (or a main unit-prism portion cutting step), thelens forming mold C is cut with the cutting tool B to form a totalreflection type prism portion forming mold placed in the first pitcharea P1 (FIG. 35A).

Thereafter, a step ST6 (or a pitch margin setting step) is performed.The step ST6 performed after the step ST2 denotes the feature of thesixth embodiment. In the step ST6, a pitch margin P1 in the first pitcharea P1 is set. Here, a pitch margin Pn+1 in the (n+1)-th pitch areaPn+1 currently cut denotes a distance in a cutting work repeatingdirection from a contacting point of the cutting tool B to a boundarypoint placed between the n-th pitch area Pn already cut and the (n+1)-thpitch area Pn+1. The vertex of the cutting tool B first comes in contact with the lens forming mold C at the contacting point when the lensforming mold C is cut with the cutting tool B to form a refraction typeprism portion forming mold (or a subsidiary unit-prism portion formingmold forming mold) placed in the (n+1)-th pitch area Pn+1.

After the pitch margin P is set in the step ST6, the procedure proceedsto a step ST7 (or a subsidiary unit-prism portion cutting step), thelens forming mold C is cut with the cutting tool B to form a refractiontype prism portion forming mold of the first pitch area P1 according tothe cutting condition (A) or the cutting condition (B) and the pitchmargin P1. In this step ST7, the cutting work is performed as is shownin FIG. 35B. As is realized by comparing the cutting work shown in FIG.35B with the cutting work shown in FIG. 33B, the refraction type prismportion forming mold is formed so as to shift the refraction type prismportion forming mold in the direction from the Fresnel center to theFresnel periphery by the pitch margin P1.

The pitch number n=2 is set in a step ST4. When the procedure returnsfrom the step ST5 to the step ST2, the cutting work for the second pitcharea P2 is performed, and the lens forming mold C is cut with thecutting tool B to form a total reflection type prism portion formingmold in the step ST2. The cutting work for the production of the totalreflection type prism portion forming mold is shown in FIG. 35C. In thesame manner as the cutting work shown in FIG. 33C, a sharp tip portionplaced on a trough line T1 is generated in this cutting work between thefirst pitch area P1 and the second pitch area P2.

In the step ST6, a pitch margin P2 (·0) of the second pitch area P2 isset (refer to FIG. 35D), and the lens forming mold C is cut with thecutting tool B to form a refraction type prism portion forming moldaccording to the pitch margin P2 in the step ST7 (refer to FIG. 35E). Inthis cutting work, the reason for setting a pitch margin in the step ST6becomes apparent.

In detail, as is realized in FIG. 35D and FIG. 35E, a cutting startposition is shifted in the direction from the Fresnel center to theFresnel periphery by the pitch margin P2 of a small width, and the lensforming mold C is cut with the cutting tool B to form the refractiontype prism portion forming mold of the second pitch area P2. Therefore,the tip portion on the trough line T1 shown within a dotted circle OK(of which an enlarged view is shown in FIG. 35F) of FIG. 35E isstrengthened to a certain degree corresponding to the pitch margin P2.Therefore, even though the pushing force of the cutting tool B isexerted on the tip portion on the trough line T1 in the direction fromthe second pitch area P2 to the first pitch area P1 in the same manneras in FIG. 33D and FIG. 33E, the tip portion placed on the trough lineT1 can have the strength resisting the pushing force of the cutting toolB.

Thereafter, until the completion of the cutting work is judged in thestep ST5, the lens forming mold C is cut with the cutting tool B at apitch margin Pn to form a refraction type prism portion forming mold ofeach pitch area Pn. Therefore, because no distortion occurs in the lensforming mold C in cases where the method of manufacturing a lens formingmold shown in FIG. 34 is adopted, the total reflection plane of eachpitch area in the Fresnel lens manufactured from the lens forming mold Ccan be formed in the shape determined in the design, and the opticalperformance of the Fresnel lens can be guaranteed.

As additional description, it is applicable that the pitch margins Pn inarbitrary n-th pitch areas Pn be set to a fixed small value or be set tocertain small values different from each other respectively.

Also, in the above drawings, as an example, the total reflection typeprism portion is set to the main unit-prism portion, and the refractiontype prism portion is set to the subsidiary unit-prism portion, and thelens forming mold C is cut in the direction from the Fresnel center tothe Fresnel periphery. However, the sixth embodiment is not restrictedto this example. For example, it is applicable that the refraction typeprism portion and the total reflection type prism portion be set to themain unit-prism portion and the subsidiary unit-prism portionrespectively and the lens forming mold C be cut in the direction fromthe Fresnel periphery to the Fresnel center.

Next, a method of suppressing the influence of distortion, which isobtained by forming a dummy prism portion forming mold in a lens formingmold for the Fresnel lens having the intermediary prism portions (referto the third embodiment), will be described.

FIG. 36A and FIG. 36B are view sex planning the configuration andoperation of a Fresnel lens having no dummy prism portion, and FIG. 37Aand FIG. 37B are views explaining the configuration and operation of aFresnel lens having dummy prism portions.

In FIG. 36A and FIG. 37A, enlarged sectional shapes of the Fresnellenses of FIG. 36A and FIG. 37A are respectively shown. Also, the heightRfl (indicated by a solid line) of the total reflection type prismportion of FIG. 36A and the height Rfr (indicated by a dot-dash line) ofthe refraction type prism portion of FIG. 36A are shown in FIG. 36B foreach pitch area, and the height Rfl (indicated by a solid line) of thetotal reflection type prism portion of FIG. 37A and the height Rfr(indicated by a dot-dash line) of the refraction type prism portion ofFIG. 37A are shown in FIG. 37B for each pitch area. The height denotes acutting depth of a prism portion in an optical axis direction of theFresnel lens. In FIG. 36A, FIG. 36B, FIG. 37A and FIG. 37B, the below inthe drawing is directed toward the Fresnel center, and the above in thedrawing is directed toward the Fresnel periphery.

In FIG. 36A and FIG. 37A, 70 indicates a Fresnel lens. Ph−1, Ph, - -,Pi−4, - -, Pi+1, - -, Pj−1, - -, and Pj+1 indicate a plurality of pitchareas of the Fresnel lens 70 respectively.

Also, 71 h−1, 71 h, - -, 71 i−4, - -, 71 i+1, - -, 71 j−1, - -, and 71j+1 indicate a plurality of total reflection type prism portions placedin the pitch areas Ph−1 to Pj+1 respectively 72 h−1, 72 h, - -, 72i−4, - -, and 72 i indicate a plurality of refraction type prismportions placed in the pitch areas Ph−1 to Pi respectively. 73 indicatesan outgoing plane of the Fresnel lens 70.

Also, only in FIG. 37A, 72 i+1, - -,72 j−1 and 72 j indicate a pluralityof refraction type prism portions (or dummy prism portions) placed inthe pitch areas Pi+1, - -, Pj−1 and Pj respectively. The heights Rfr ofthe refraction type prism portions 72 i+1 to 72 j are set to a low value(Rfr=0) as compared with the heights Rfl of the total reflection typeprism portions 71 i+1 to 71 j, and the refraction type prism portions 72i+1 to 72 j have no participation in the reception of rays of incidentlight.

In FIG. 36A and FIG. 37A, because the Fresnel lens 70 is manufactured byusing the lens forming mold C manufactured without any pitch margin, itis realized that distortion (within dotted circles NG) occurs in thetotal reflection planes of the total reflection type prism portions 71h−1 to 71 i−1 when the refraction type prism portions 72 h−1 to 72 i arecut (in the drawings, the shape of each distorted portion is linearlyshown).

In addition, in the Fresnel lens 70 shown in FIG. 37A, the refractiontype prism portions 72 hi+1 to 72 j are additionally arranged.Therefore, in addition to the distortion of the total reflection typeprism portions 71 h−1 to 71 i−1, distortion (within dotted circles NG)occurs in the total reflection planes of the total reflection type prismportions 71 i to 71 j−1. The refraction type prism portions 72 i+1 to 72j are intentionally arranged in the pitch areas Pi+1 to Pj. Theexistence of the refraction type prism portions 72 i+1 to 72 j denotesthe difference between the Fresnel lens 70 shown in FIG. 36A and theFresnel lens 70 shown in FIG. 37A.

In FIG. 36A, rays of light are incident at comparatively small incidentangles on a group of center side pitch areas ranging from the pitch areaPi−4 to the Fresnel center. Therefore, a plurality of hybrid type prismportions having the total reflection type prism portions 71 i−4, - -, 71h, 71 h−1, - - and the refraction type prism portions 72 i−4, - -, 72 h,72 h−1, - - are formed in the group of center side pitch areas. As shownin FIG. 36A, the ratio of the height RF1 to the height RFr in the groupof center side pitch areas having the total reflection type prismportions 71 i−4, - -, 71 h, 71 h−1, - - and the refraction type prismportions 72 i−4, - -, 72 h, 72 h−1, - - is set to 1:1.

In contrast, in FIG. 36A, rays of light are incident at comparativelylarge incident angles on a group of periphery side pitch areas rangingfrom the pitch area Pi+1 to the Fresnel periphery. Because a refractiontype prism portion hardly functions as a lens due to the deteriorationof the transmissivity for a large incident angle, the height Rfr of therefraction type prism portion is set to zero (refer to FIG. 36B).Therefore, only the total reflection type prism portions 71 i+1, - -, 71j−1, 71 j, 71 j+1, - - are formed in the group of periphery side pitchareas.

Also, as shown in FIG. 36B, in a group of intermediary pitch areasranging from the pitch area Pi−3 to the pitch area Pi which are placedin a transient region from the group of center side pitch areas to thegroup of periphery side pitch areas shown in FIG. 36A, the height Rfr ofeach of there fraction type prism portions 72 i−3 to 72 i is graduallydecreased in the direction from the Fresnel center side pitch area tothe Fresnel periphery side pitch area, and a plurality of hybrid typeprism portions (or a plurality of intermediary prism portions) havingthe refraction type prism portions 72 i−3 to 72 i are formed. The reasonfor gradually decreasing the height Rfr is to smoothly changetransmissivity characteristics of the hybrid type prism portions in thetransient region from the group of center side pitch areas to the groupof periphery side pitch areas. Because the group of intermediary prismportions is arranged in the Fresnel lens 70 shown in FIG. 36A,transmissivity characteristics of the hybrid type prism portions can besmoothly changed fundamentally.

However, because distortion indicated within the dotted circles NGoccurs in the total reflection planes of the total reflection type prismportions 71 h−1 to 71 i−1, discontinuity between the transmissivity ofthe pitch area Pi−1 and the transmissivity of the pitch area Pi becomeslarge in the Fresnel lens 70 shown in FIG. 36A. Therefore, in caseswhere the Fresnel lens 70 shown in FIG. 36A is applied to a screen, anunnatural boundary line is undesirably generated in the brightness of animage displayed on the screen.

In contrast, in the Fresnel lens 70 shown in FIG. 37A, it is presumedthat distortion indicated within the dotted circles NG occurs in thetotal reflection planes of the total reflection type prism portions ofthe Fresnel lens 70 shown in FIG. 37A, and the refraction type prismportions 72 i+1 to 72 j are intentionally arranged in addition to theconfiguration of the Fresnel lens 70 shown in FIG. 36A. Therefore,discontinuity in transmissivity between pitch areas can be avoided inthe Fresnel lens 70 shown in FIG. 37A in the different manner from thatin the Fresnel lens 70 shown in FIG. 36A.

The difference between the Fresnel lens 70 of FIG. 37A and the Fresnellens 70 of FIG. 36A will be described in more detail.

FIG. 38A and FIG. 38B are views explaining the difference between theFresnel lens 70 of FIG. 37A and the Fresnel lens 70 of FIG. 36A. FIG.38A is an enlarged view of the pitch areas Pi−1 to Pj in the Fresnellens 70 of FIG. 36A, and FIG. 38B is an enlarged view of the pitch areasPi−1 to Pj in the Fresnel lens 70 of FIG. 37A. The constituent elements,which are the same as those shown in FIG. 36A or FIG. 37A, are indicatedby the same reference numerals as those of the constituent elementsshown in FIG. 36A or FIG. 37A.

In the pitch area Pi−1 of FIG. 38A, because the final refraction typeprism portion 72 i is arranged in the pitch area Pi adjacent to thepitch area Pi−1 on the Fresnel periphery side, distortion indicated by adotted circle NG occurs in the total reflection plane 74 i−1 of thetotal reflection type prism portion 71 i−1. Therefore, all the flux ofincident light 76 i−1 received on the incident plane 75 i−1 of the totalreflection type prism portion 71 i−1 is not totally reflected on thetotal reflection plane 74 i−1 to go out from the outgoing plane 73. Inother words, a part of the flux of incident light 76 i−1 refracted onthe incident plane 75 i−1 is scattered on the total reflection plane 74i−1 due to the distortion indicated by the dotted circle NG in adirection different from a total reflection direction originally set.Therefore, loss of the light is caused in the pitch area Pi−1.

In contrast, in the pitch area Pi of FIG. 38A, because no refractiontype prism portion 72 i is arranged in the pitch area Pi+1 adjacent tothe pitch area Pi on the Fresnel periphery side, no distortion occurs inthe total reflection plane 74 i of the total reflection type prismportion 71 i. Therefore, all the flux of incident light 76 i received onthe incident plane 75 i of the total reflection type prism portion 71 iis totally reflected on the total reflection plane 74 i and goes outfrom the outgoing plane 73. Therefore, no loss of the light is caused inthe pitch area Pi in the different manner from that in the pitch areaPi−1.

In the same manner, in the pitch are as Pi+1, - - of FIG. 38A, nodistortion occurs in the total reflection planes 74 i+1, - -. Therefore,discontinuity in the transmissivity between the pitch area Pi−1 havingthe loss of the light due to the distortion and the pitch area Pi havingno loss of the light becomes large.

In contrast to the case of FIG. 38A, in the Fresnel lens 70 shown inFIG. 38B, it is presumed that distortion indicated within a dottedcircle NG occurs in the total reflection plane 74 i, and the refractiontype prism portion 72 i+1 having no participation in the reception oflight is intentionally arranged in the pitch area Pi+1 adjacent to thepitch area Pi on the Fresnel periphery side. Therefore, a partial fluxof light 77 i is refracted on the incident plane 75 i and is scatteredon the total reflection plane 74 i due to the distortion indicated bythe dotted circle NG in a direction different from a total reflectiondirection originally set. Therefore, loss of the light is caused in thepitch area Pi in the same manner as in the pitch area Pi−1, anddiscontinuity in the transmissivity is avoided.

In the same manner, the refraction type prism portions 72 i+2, - -, 72j−1 and 72 j having no participation in the reception of light arearranged in the pitch areas Pi+2, - -, Pj−1 and Pj placed on the Fresnelperiphery side of the pitch area Pi+1, and discontinuity in thetransmissivity is avoided. Also, because incident angles of rays ofincident light in remaining pitch areas placed on the Fresnel peripheryside of the pitch areas Pi+2, - -, Pj−1 and Pj become sufficiently largein the Fresnel lens 70, no total reflection is performed on the wholetotal reflection plane of each remaining pitch area. Therefore, eachremaining pitch area has no dummy refractive type prism portion.

The pitch area Pj of FIG. 38B just corresponds to no total reflection onthe whole total reflection plane. Because the incident angles of therays of incident light are sufficiently large in the pitch area Pj, aportion of the total reflection plane 74 j, in which the occurrence ofdistortion indicated by a dotted circle NG is expected, is not used forthe total reflection of the incident light. Therefore, the difference inthe light loss between the pitch area Pj and an adjacent pitch area Pj−1has no connection with the existence of distortion indicated by a dottedcircle NG.

Accordingly, because the refraction type prism portions 72 i+1, - -,72j−1 and 72 j having no participation in the reception of light arearranged in the pitch areas Pi+1, - -, Pj−1 and Pj in which the totalreflection type prism portions 71 i+1, - -, 71j−1 and 71 j are arranged,discontinuity in the transmissivity due to the distortion indicated bythe dotted circles NG can be prevented.

As is described above, in the sixth embodiment, the step ST6 for settingthe pitch margin .Pn is set after the step ST2, a cutting start positionis shifted in a cutting performing direction by the pitch margin. P2,and each subsidiary unit-prism portion is cut in the step ST7.Therefore, when the subsidiary unit-prism portion is cut, distortion ofthe lens forming mold C occurring in the tip portion of the trough lineTn placed between main unit-prism portions for each pitch area can beprevented. Accordingly, the lens forming mold C can be formed in a shapedetermined in the design step, and the optical performance of theFresnel lens manufactured from the lens forming mold C can beguaranteed.

Also, in the sixth embodiment, the hybrid type prism portions having thetotal reflection type prism portions and the refraction type prismportions are formed in the group of Fresnel center side pitch areas,only the total reflection type prism portions are formed in the group ofFresnel periphery side pitch areas, the height of each total reflectiontype prism portion is set to a fixed value in the group of intermediarypitch areas, and the height of each of the refraction type prismportions is gradually decreased in the group of intermediary pitch areasin the direction from the group of Fresnel center side pitch areas tothe group of Fresnel periphery side pitch areas. In cases where thegroup of Fresnel center side pitch areas, the group of Fresnel peripheryside pitch areas and the group of intermediary pitch areas aremanufactured, the refraction type prism portions having a minimum heightin the group of intermediary pitch areas and having no participation inthe reception of the light are formed by the cutting work as dummy prismportions in the pitch areas ranging from the group of intermediary pitchareas to apart of the group of Fresnel periphery side pitch areas.Accordingly, discontinuity in the transmissivity due to the light losscaused by the distortion of the total reflection planes can beprevented.

In the sixth embodiment, the dummy prism portions are formed by thecutting work in the pitch areas ranging from the group of intermediarypitch areas to the group of Fresnel periphery side pitch areas. However,the sixth embodiment is not restricted to this feature. For example, incases where the shape of the prism portion is changed for each pitcharea to transfer from the shape of the hybrid type prism portion(including the intermediary prism portion) to the shape of either therefraction type prism portion or the total reflection prism portion orto transfer from the shape of either the refraction type prism portionor the total reflection prism portion to the shape of the hybrid typeprism portion (including the intermediary prism portion), dummy prismportions are successively arranged in a part of the group of pitch areasin which the shape of the prism portion is changed. Therefore, a rapidis appearance and occurrence of a manufacturing error occurring by thechange of the shape of the prism portion can be suppressed, and a rapidchange of the optical performance such as transmissivity can berelieved.

Embodiment 7

As is described in the first embodiment, the refraction type prismportion has the ineffective plane, the flux of incident light (or agroup of rays of ineffective light) received on the ineffective plane ischanged to stray light in the inside of the Fresnel lens, and the straylight goes out from the outgoing plane. Therefore, the ineffective planegenerates ghosts on the screen. Also, according to conditions of theincident angle of the incident light, there is a case where there is agroup of rays of light which is transmitted through the total reflectiontype prism portion but is not totally reflected on the total reflectionplane. The group of rays is vulgarly expressed as striking-at-the-airrays not striking at the total reflection plane. The group of rays isalso changed to stray light, and ghosts are generated on the screen. Ina seventh embodiment, a Fresnel lens having a structure of absorbingstray light and reducing ghosts on the incident side or the outgoingside will be described.

FIG. 39 is a view showing a sectional shape of a Fresnel lens accordingto a seventh embodiment of the present invention. A structure ofreducing ghosts caused from rays of ineffective light is arranged on theincident side of the Fresnel lens 1. The constituent elements, which arethe same as those shown in FIG. 9, are indicated by the same referencenumerals as those of the constituent elements shown in FIG. 9.

In FIG. 39, 81 indicates a light absorbing layer arranged in each of theineffective planes 3Z, 3Z−1, - - of the refractive type prism portions3A, - -.

The light absorbing layer 81 absorbs rays of ineffective light Lieincident on each of the ineffective planes 3Z, 3Z−1, - - of the pitchareas. Because the light absorbing layers 81 are arranged on theineffective planes 3Z, 3Z−1, - - respectively, the generation of straylight in the inside of the Fresnel lens 1 can be prevented, and ghostsgenerated on the screen can be reduced.

FIG. 40 is a view showing a sectional shape of another Fresnel lensaccording to the seventh embodiment of the present invention. Astructure of absorbing stray light derived from rays of ineffectivelight or swishing-the-air rays on the outgoing plane is shown. Theconstituent elements, which are the same as those shown in FIG. 9, areindicated by the same reference numerals as those of the constituentelements shown in FIG. 9.

In FIG. 40, 82 indicates a stray light absorbing plate arranged on theoutgoing plane 5 of the Fresnel lens 1. The stray light absorbing plate82 is formed of a plane parallel plate having both an incident plane andan outgoing plane parallel to the outgoing plane 5 of the Fresnel lens1.A plurality of light transmitting layers 83 and a plurality of thin-filmlight absorbing layers 84 are alternately layered in the stray lightabsorbing plate 82 so as to be parallel to the optical axis (not shown)of the Fresnel lens 1. Rays of light transmit through each lighttransmitting layer 83, and rays of light are absorbed in each lightabsorbing layer 84.

As shown in FIG. 40, as compared with both an optical path of a ray oflight b3 received on the incident plane 3B of the refraction type prismportion 3A and an optical path of a ray of light b4 received on theincident plane 4B of the total reflection type prism portion 4A, a rayof stray light be1 is generated in the inside of the Fresnel lens 1 froma ray of light incident on each ineffective plane 3Z, 3Z-1, - -, a rayof stray light be2 is generated from a striking-at-the-air ray which isincident on the incident plane 4B of the total reflection type prismportion 4A and does not strike at the total reflection plane 4C, and theray of stray light be1 and the ray of stray light be2 propagated throughthe. Fresnel lens 1 are greatly inclined toward a radial direction ofthe Fresnel lens 1. Therefore, when the ray of stray light be1 and theray of stray light be2 go out from the outgoing plane 5 of the Fresnellens 1 and are changed to rays of light be1′ and be2′ respectively, therays of light be1′ and be2′ are absorbed in the light absorbing layer 84layered in parallel to the optical axis of the Fresnel lens 1.

Also, the ray of light b3 received on the incident plane 3B of therefraction type prism portion 3A and the ray of light b4 received on theincident plane 4B of the total reflection type prism portion 4A go outfrom the outgoing plane 5 and are changed to rays of light b3′ and b4′,and parts of the rays of light b3′ and b4′ are absorbed in the lightabsorbing layer 84. However, because the rays of light b3′ and b4′ goout almost in parallel to the optical axis of the Fresnel lens 1, anamount of the rays of light b3′ and b4′ absorbed in the light absorbinglayer 84 is very small. Therefore, the greater parts of the rays oflight b3′ and b4′ are transmitted through the light transmitting layer83 and are propagated to the lenticular (not shown). Therefore, there isno great problem.

Here, as shown in FIG. 41A, it is applicable that the layered structureof the light transmitting layers 83 and the light absorbing layers 84 beformed in a concentric circular shape (or a radial manner) by placingthe optical axis of the Fresnel lens 1 in the center of concentriccircles. Also, as shown in FIG. 41B, it is applicable that the lighttransmitting layers 83 and the light absorbing layers 84 be layered inupper and lower directions in FIG. 41B so as to extend each of thelayers 83 and 84 in right and left directions in FIG. 41B. In this case,when the Fresnel lens 1 is applied to a screen having an aspect ratio of3:4, a ratio of the length in upper and lower directions to the lengthin right and left directions is 3:4.

In cases where the configuration of the Fresnel lens 1 shown in FIG. 41Ais adopted, an absorption efficiency of the stray light can bemaximized. Also, in cases where the configuration of the Fresnel lens 1shown in FIG. 41B is adopted, the stray light absorbing plate 82 can beeasily manufactured, and a manufacturing cost can be reduced.

Also, it is applicable that a layered interval between each pair of thelight absorbing layers 84 adjacent each other (or a thickness of eachlight transmitting layer 83) be set to the pitch of the Fresnel lens 1or be changed according to a distance between the optical axis of theFresnel lens 1 and the pair of the light absorbing layers 84. In otherwords, the layered interval between each pair of the light absorbinglayers 84 can be freely designed according to specifications. Inaddition, the pitch of the light absorbing layers 84 in the layeredstructure should be set so as to prevent moire fringes from occurringdue to the interference with a periodical structure of the lenticular(not shown).

Also, it is applicable that a plurality of slits used for the embeddingof the light absorbing layers 84 be arranged on the side of the outgoingplane 5 of the Fresnel lens 1 in case of the layered pattern shown inFIG. 41A or FIG. 41B and the light absorbing layers 84 be arranged inthe slits. In this case, it is preferred that paint having a lightabsorbing performance is packed in the slits to form the light absorbinglayers 84. Therefore, because the stray light absorbing plate 82arranged on the outgoing plane 5 of the Fresnel lens 1 is integrallyformed with the Fresnel lens 1, the number of constituent parts can bereduced.

FIG. 42 is a view showing a sectional shape of another Fresnel lensaccording to the seventh embodiment of the present invention. Astructure of absorbing stray light, which is generated from rays oflight received on the ineffective plane, on the side of the outgoingplane is shown. The constituent elements, which are the same as thoseshown in FIG. 9 or FIG. 40, are indicated by the same reference numeralsas those of the constituent elements shown in FIG. 9 or FIG. 40.

In FIG. 42, 85 indicates a light absorbing plate arranged on the side ofthe outgoing plane 5 of the Fresnel lens 1. The light absorbing plate 85is formed of a plane parallel plate having both an incident plane and anoutgoing plane parallel to the outgoing plane 5 of the Fresnel lens 1.

As is described with reference to FIG. 40, the ray of stray light be1and the ray of stray light be2 propagated through the Fresnel lens 1 aregreatly inclined toward a radial direction of the Fresnel lens 1.Therefore, as compared with both an optical path length B3′ of the rayof light b3′ received on the incident plane 3B of the refraction typeprism portion 3A and going out from the outgoing plane 5 and an opticalpath B4′ length of the ray of light b4′ received on the incident plane4B of the total reflection type prism portion 4A and going out from theoutgoing plane 5, optical patching ths BE1′ and BE2′ of the rays ofstray light be1′ and be2′ propagated through the light absorbing plate85 are longer than the optical path lengths B3′ and B4′. Therefore, theabsorption of the stray light be1′ and be2′ in the light absorbing plate85 is larger than that of the light b3′ and b4′ by a degreecorresponding to the difference between the optical path length BE1′ orBE2′ and the optical path length B3′ or B4′, and the intensity of therays of the stray light be1′ and be2′ going out from the light absorbingplate 85 can be reduced.

Also, optical path lengths of rays of the stray light be3 and be4reflected many times in the inside (or on the outgoing plane) of thelight absorbing plate 85 are further lengthened to a degreecorresponding to the number of reflections, and the rays of the straylight be3 and be4 are largely absorbed in the light absorbing plate 85.Therefore, the intensity of the rays of the stray light be3 and be4 islowered than that of the rays of the stray light be1′ and be2′, andthere is no problem.

Also, rays of the stray light be5 and be6 reflected on the side of theincident plane of the light absorbing plate 85 are refracted andreflected (many times) in various portions of the Fresnel lens 1 and areincident on the light absorbing plate 85. Therefore, the intensity ofrays of light refracted and reflected in various portions of the Fresnellens 1 and going out from the Fresnel lens 1 is further reduced by aloss received due to the refraction and reflection in the variousportions of the Fresnel lens 1.

Therefore, the stray light can be absorbed in a simple structure byusing the light absorbing plate 85, and ghosts generated on the screencan be reduced.

Here, it is applicable that the structures of reducing the ghosts shownin FIG. 39 to FIG. 42 be arbitrarily combined to absorb the stray light.For example, the combination of the light absorbing layers 81 and thestray light absorbing plate 82 or the combination of the light absorbinglayers 81 and the light absorbing plate 85 is applied to the Fresnellens 1. In this case, the stray light can be further absorbed, andghosts generated on the screen can be further reduced.

As is described above, in the seventh embodiment, the thin-film typelight absorbing layers 81 used to absorb light are arranged on theineffective planes 3Z, 3Z−1, - - of the refraction type prism portions3A respectively. Therefore, the generation of stray light in the insideof the Fresnel lens 1 can be prevented, and ghosts generated on thescreen can be reduced.

Also, in the seventh embodiment, the stray light absorbing plate 82having the plurality of light absorbing layers 84 and the plurality oflight transmitting layers 83 alternately arranged and respectivelylayered almost in parallel to the optical axis of the Fresnel lens 1 isarranged on the outgoing plane 5. Therefore, the stray light generatedin the inside of the Fresnel lens 1 can be absorbed, and ghostsgenerated on the screen can be reduced.

Also, in the seventh embodiment, because the stray light absorbing plate82 is arranged on the outgoing plane 5 of the Fresnel lens 1 and isintegrally formed with the Fresnel lens 1, the stray light can beabsorbed by using a structure in which the number of constituent partsis small.

Also, in the seventh embodiment, the light transmitting layers 83 andthe light absorbing layers 84 are layered in a concentric circular shape(or a radial manner) by placing the optical axis of the Fresnel lens 1in the center of concentric circles. Accordingly, an absorptionefficiency of the stray light can be maximized.

Also, in the seventh embodiment, the light transmitting layers 83 andthe light absorbing layers 84 are layered in parallel tone direction.Accordingly, the stray light absorbing plate 82 can be easilymanufactured, and a manufacturing cost of the stray light absorbingplate 82 can be reduced.

Also, in the seventh embodiment, because the light absorbing plate 85 isarranged on the outgoing plane 5 of the Fresnel lens 1, the stray lightcan be absorbed in a simple structure using the light absorbing plate85, and ghosts generated on the screen can be reduced.

INDUSTRIAL APPLICABILITY

As is described above, the Fresnel lens according to the presentinvention is appropriate to a rear projection type projection system inwhich rays of image light are projected on to a screen from the rearside of the screen.

What is claimed is:
 1. A method of manufacturing a lens forming mold, inwhich a lens forming mold is cut in a reversed shape of both arefractive prism portion and a total reflection type prism portionformed for each pitch area of a Fresnel lens by using a cutting tool,comprising: a main unit-prism portion cutting step of cutting the lensforming mold in a reversed shape of the refractive prism portion of acutting pitch area by using the cutting tool; and a subordinateunit-prism portion cutting step of cutting the lens forming mold in areversed shape of the total reflection prism portion of the cuttingpitch area by using the cutting tool when a plane, obtained by extendingan incident plane from the cutting pitch area in the reversed shape ofthe total reflection prism portion, intersects a trough line placedbetween the cutting pitch area and another cutting area adjacent to thecutting pitch area on a Fresnel center side or when the plane passesthrough an area shifted from the trough line toward a light outgoingside, wherein the-combination of the main unit-prism portion cuttingstep and the subordinate unit-prism portion cutting step is repeatedlyperformed by a prescribed number equal to the number of cutting pitchareas.
 2. A method of manufacturing a lens forming mold, in which a lensforming mold is cut in a reversed shape of both a refractive prismportion and a total reflection prism portion formed for each pitch areaof a Fresnel lens by using a cutting tool, comprising: a main unit-prismportion cutting step of cutting the lens forming mold in a reversedshape of the total reflection prism portion of a cutting pitch area byusing the cutting tool; and a subordinate unit-prism portion cuttingstep of cutting the lens forming mold in a reversed shape of therefractive prism portion of the cutting pitch area by using the cuttingtool when a plane, obtained by extending an incident plane from thecutting pitch area in the reversed shape of the total refractive prismportion, intersects a trough line placed between the cutting pitch areaand another cutting area adjacent to the cutting pitch area on a Fresnelperiphery side or when the plane passes through an area shifted from thetrough line toward a light outgoing side, wherein the combination of themain unit-prism portion cutting step and the subordinate unit-prismportion cutting step is repeatedly performed by a prescribed numberequal to the number of cutting pitch areas.
 3. The method ofmanufacturing a lens forming mold according to claim 1, furthercomprising: a pitch margin setting step for setting a pitch margin foreach cutting pitch area before the subordinate unit-prism portioncutting step in cases where the lens forming mold is cut in a cutperforming direction from the Fresnel periphery side to a Fresnel centerside in the order of the refractive prism portion and the totalreflection type prism portion, wherein the subordinate unit-prismportion cutting step comprises the steps of: shifting a cutting startposition toward the cut performing direction by the pitch margin; andcutting the lens forming mold to form the reversed shape of the totalreflection prism portion for each cutting pitch area.
 4. The method ofmanufacturing a lens forming mold according to claim 2, furthercomprising: a pitch margin setting step for setting a pitch margin foreach cutting pitch area before the subordinate unit-prism portioncutting step in cases where the lens forming mold is cut in a cutperforming direction from a Fresnel center side to the Fresnel peripheryside in the order of the total reflection prism portion and therefractive prism portion, wherein the subordinate unit-prism portioncutting step comprises the steps of: shifting a cutting start positiontoward the cut performing direction by the pitch margin; and cutting thelens forming mold to form the reversed shape of the refractive prismportion for each cutting pitch area.
 5. The method of manufacturing alens forming mold according to claim 2, further comprising the step of:successively cutting the lens forming mold in a reversed shape of aplurality of dummy prism portions respectively having a height in anoptical axis direction not participated in the reception of light for agroup of pitch areas.
 6. A method of manufacturing a lens, comprisingthe steps of: pouring resin into a lens forming mold manufactured in themethod of manufacturing a lens forming mold according to claim 1;hardening the resin; and taking off the lens forming mold from thehardened resin to form a lens.
 7. A method of manufacturing a lens,comprising the steps of: pouring resin into a lens forming moldmanufactured in the method of manufacturing a lens forming moldaccording to claim 2; hardening the resin; and taking off the lensforming mold from the hardened resin to form a lens.
 8. A method ofmanufacturing a lens, comprising the steps of: pouring resin into a lensforming mold manufactured in the method of manufacturing a lens formingmold according to claim 3; hardening the resin; and taking off the lensforming mold from the hardened resin to form a lens.
 9. A method ofmanufacturing a lens, comprising the steps of: pouring resin into a lensforming mold manufactured in the method of manufacturing a lens formingmold according to claim 4; hardening the resin; and taking off the lensforming mold from the hardened resin to form a lens.
 10. A method ofmanufacturing a lens, comprising the steps of: pouring resin into a lensforming mold manufactured in the method of manufacturing a lens formingmold according to claim 5; hardening the resin; and taking off the lensforming mold from the hardened resin to form a lens.